New articles on quant-ph

[1] 2007.01881

Classical/quantum correspondence for pseudo-hermitian systems

In this work, a classical/quantum correspondence for a pseudo-hermitian system with finite energy levels is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-hermitian Hamiltonian if there is a suitable canonical transformation that links it to a real field. We construct a covariant quantization scheme which maps canonically related pseudoclassical theories to unitarily equivalent quantum realizations, such that there is a unique metric-inducing isometry between the distinct Hilbert spaces. In this setting, the pseudo-hermiticity condition for the operators induces an involution which guarantees the reality of the corresponding symbols, even for the complex field case. We assign a physical meaning for the dynamics in the presence of a complex field by constructing a classical correspondence. As an application of our theoretical framework, we propose a damped version of the Rabi problem and determine the configuration of the parameters of the setup for which damping is completely suppressed.

[2] 2007.01882

Quantum fluctuations hinder finite-time information erasure near the Landauer limit

Information is physical but information is also processed in finite time. Where computing protocols are concerned, finite-time processing in the quantum regime can dynamically generate coherence. Here we show that this can have significant thermodynamic implications. We demonstrate that quantum coherence generated in the energy eigenbasis of a system undergoing a finite-time information erasure protocol yields rare events with extreme dissipation. These fluctuations are of purely quantum origin. By studying the full statistics of the dissipated heat in the slow driving limit, we prove that coherence provides a non-negative contribution to all statistical cumulants. Using the simple and paradigmatic example of single bit erasure, we show that these extreme dissipation events yield distinct, experimentally distinguishable signatures.

[3] 2007.01901

Quantifying the sensitivity to errors in analog quantum simulation

Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections. Here we propose a framework to characterize the performance of quantum simulators by linking robustness of quantum expectation values to the spectral properties of the output observable, which in turn can be associated with its macroscopic or microscopic character. We show that, under general assumptions and on average over all states, imperfect devices are able to reproduce the dynamics of macroscopic observables accurately, while the relative error in the expectation value of microscopic observables is much larger on average. We experimentally demonstrate the universality of these features in a state-of-the-art quantum simulator and show that the predicted behavior is generic for a highly accurate device, without assuming any knowledge about the nature of the imperfections.

[4] 2007.01964

Self-amplifying spin measurement in a long-lived spin-squeezed state

Using the platform of a trapped-atom clock on a chip, we have generated spin-squeezed states with up to 8.1(9) dB of metrological squeezing in a cloud of $2\times 10^4$ ultracold alkali atoms by quantum nondemolition (QND) measurement in a fiber Fabry-Perot microcavity. Observing the time evolution of the squeezed state on unprecedented timescales of more than one second reveals a surprising measurement amplification effect in the final measurement of the spin state. It results from a subtle interplay between the spin dynamics of interacting indistinguishable particles and energy-dependent cavity coupling and leads to an increased cavity shift per spin, and thus to a higher signal per photon read out. Metrological spin squeezing is preserved for 1 s. Both results open up encouraging perspectives for squeezing-enhanced atomic clocks in a metrologically relevant stability regime.

[5] 2007.01966

Limitations in quantum computing from resource constraints

Fault-tolerant quantum computation is the only known route to large-scale, accurate quantum computers. Fault tolerance schemes prescribe how, by investing more physical resources and scaling up the size of the computer, we can keep the computational errors in check and carry out more and more accurate calculations. Underlying all such schemes is the assumption that the error per physical gate is independent of the size of the quantum computer. This, unfortunately, is not reflective of current quantum computing experiments. Here, we examine the general consequences on fault-tolerant quantum computation when constraints on physical resources, such as limited energy input, result in physical error rates that grow as the computer grows. In this case, fault tolerance schemes can no longer reduce computational error to an arbitrarily small number, even if one starts below the so-called fault tolerance noise threshold. Instead, there is a minimum attainable computational error, beyond which further growth of the computer in an attempt to reduce the error becomes counter-productive. We discuss simple, but rather generic, situations in which this effect can arise, and highlight the areas of future developments needed for experiments to overcome this limitation.

[6] 2007.01989

Stable Polarization Entanglement based Quantum Key Distribution over Metropolitan Fibre Network

We demonstrate a quantum key distribution implementation over deployed dark telecom fibers with polarisation-entangled photons generated at the O-band. One of the photons in the pairs are propagated through 10km of deployed fiber while the others are detected locally. Polarisation drifts experienced by the photons propagating through the fibers are compensated with liquid crystal variable retarders. This ensures continuous and stable QKD operation with an average QBER of 6.4% and a final key rate of 109 bits/s.

[7] 2007.01997

Universal non-Markovianity Detection in Hybrid Open Quantum Systems

A universal characterization of non-Markovianity for any open hybrid quantum systems is presented. This formulation is based on the negativity volume of the generalized Wigner function, which serves as an indicator of the quantum correlations in any composite quantum systems. It is shown, that such defined measure can be utilized for any single or multi-partite quantum system, containing any discrete or continuous variables. To demonstrate its power in revealing non-Markovianity in such quantum systems, we additionally consider a few illustrative examples.

[8] 2007.02027

Single-Atom Verification of the Information-Theoretical Bound of Irreversibility at the Quantum Level

Quantitative measure of disorder or randomness based on the entropy production characterizes thermodynamical irreversibility, which is relevant to the conventional second law of thermodynamics. Here we report, in a quantum mechanical fashion, the first theoretical prediction and experimental exploration of an information-theoretical bound on the entropy production. Our theoretical model consists of a simplest two-level dissipative system driven by a purely classical field, and under the Markovian dissipation, we find that such an information-theoretical bound, not fully validating quantum relaxation processes, strongly depends on the drive-to-decay ratio and the initial state. Furthermore, we carry out experimental verification of this information-theoretical bound by means of a single spin embedded in an ultracold trapped $^{40}$Ca$^{+}$ ion. Our finding, based on a two-level model, is fundamental to any quantum thermodynamical process and indicates much difference and complexity in quantum thermodynamics with respect to the conventionally classical counterpart.

[9] 2007.02139

Quantum simulations with complex geometries and synthetic gauge fields in a trapped ion chain

In recent years, arrays of atomic ions in a linear RF trap have proven to be a particularly successful platform for quantum simulation. However, a wide range of quantum models and phenomena have, so far, remained beyond the reach of such simulators. In this work we introduce a technique that can substantially extend this reach using an external field gradient along the ion chain and a global, uniform driving field. The technique can be used to generate both static and time-varying synthetic gauge fields in a linear chain of trapped ions, and enables continuous simulation of a variety of coupling geometries and topologies, including periodic boundary conditions and high dimensional Hamiltonians. We describe the technique, derive the corresponding effective Hamiltonian, propose a number of variations, and discuss the possibility of scaling to quantum-advantage sized simulators. Additionally, we suggest several possible implementations and briefly examine two: the Aharonov-Bohm ring and the frustrated triangular ladder.

[10] 2007.02150

Classical and quantum analysis of the parametric oscillator with Morse-like time-dependent frequency

We consider the problem of understanding the basic features displayed by quantum systems described by parametric oscillators whose time-dependent frequency parameter $\omega(t)$ varies during evolution so to display either a non harmonic hole or barrier. To this scope we focus on the case where $\omega(t)^2$ behaves like a Morse potential, up to possible sign reversion and translations in the $(t,\omega^2)$ plane. We derive closed form solution for the time-dependent amplitude of quasi-normal modes, that is known to be the very fundamental dynamical object entering the description of both classical and quantum dynamics of time-dependent quadratic systems. Once such quantity is determined and its significant characteristics highlighted, we provide a more refined insight on the way quantum states evolve by paying attention on the position-momentum Heisenberg uncertainty principle and the statistical aspects implied by second-order correlation functions over number-type states.

[11] 2007.02159

Generation and dynamics of entangled fermion-photon-phonon states in nanocavities

We develop the analytic theory describing the formation and evolution of entangled quantum states for a fermionic quantum emitter coupled to a quantized electromagnetic field in a nanocavity and quantized phonon or mechanical vibrational modes. The theory is applicable to a broad range of cavity quantum optomechanics problems and emerging research on plasmonic nanocavities coupled to single molecules and other quantum emitters. The optimal conditions for a tri-state entanglement are realized near the parametric resonances in a coupled system. The model includes decoherence effects due to coupling of the fermion, photon, and phonon subsystems to their dissipative reservoirs within the stochastic evolution approach, which is derived from the Heisenberg-Langevin formalism. Our theory provides analytic expressions for the time evolution of the quantum state and observables, and the emission spectra. The limit of a classical acoustic pumping and the interplay between parametric and standard one-photon resonances are analyzed.

[12] 2007.02176

Quantum particles that behave as free classical particles

The existence of non--vanishing Bohm potentials, in the Madelung--Bohm version of the Schr\"odinger equation, allows for the construction of particular solutions for states of quantum particles interacting with non--trivial external potentials whose propagation is equivalent to the one for classical free particles.

[13] 2007.02182

A new approach to solving the Schrödinger equation

A new approach to find exact solutions to one--dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. The potential function defines the amplitude and the phase of any wavefunction which solves the one--dimensional Schr\"odinger equation. This new approach allows us to recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions that have vanishing and non--vanishing Bohm potentials. For most of the potentials, no solutions to the Schr\"odinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some unexpected and surprising quantum results which seem to (but do not) violate the correspondence principle such as accelerated Airy wavefunctions which solve the free Schr\"odinger equation, are due to the presence of non--vanishing Bohm potentials. New examples of this kind are found and discussed. The relation of these results to some of the unusual solutions to other wave equations is briefly discussed.

[14] 2007.02217

The thermodynamics of clocks

All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks require large energy dissipation. For periodic clocks, operating on a limit cycle, this is a consequence of phase diffusion. It is also true for non periodic clocks (for example, radio carbon dating) but due to telegraph noise not to phase diffusion. In this case a key role is played by accurate measurements that decrease entropy, thereby raising the free energy of the clock, and requires access to a low entropy reservoir. In the quantum case, for which thermal noise is replaced by quantum noise (spontaneous emission or tunnelling), measurement plays an essential role for both periodic and non periodic clocks. The paper concludes with a discussion of the Tolman relations and Rovelli's thermal time hypothesis in terms of clock thermodynamics.

[15] 2007.02218

Robust Preparation of Many-body Ground States in Jaynes-Cummings Lattices

Strongly-correlated polaritons in Jaynes-Cummings (JC) lattices can exhibit quantum phase transitions between the Mott-insulating and the superfluid phases at integer fillings. Here we present an approach for the robust preparation of many-body ground states of polaritons in a finite-sized JC lattice by optimized nonlinear ramping. In the deep Mott-insulating and deep superfluid regimes, polaritons can be pumped into a JC lattice and be prepared in the ground state with high accuracy via engineered pulse sequences. Using such states as initial state and employing optimized nonlinear ramping, we demonstrate that many-body ground states in the intermediate regimes of the parameter space can be generated with high fidelity. We exploit a Landau-Zener-type of estimation on this finite-sized system and derive an optimal ramping index for selected ramping trajectories, which greatly improves the fidelity of the prepared states. With numerical simulation of the ramping process, we further show that by choosing an appropriate trajectory, the fidelity can remain close to unity in almost the entire parameter space. This method is general and can be applied to many other systems.

[16] 2007.02229

Bilayer graphene coherent states

In this paper we consider the interaction of electrons in bilayer graphene with a constant homogeneous magnetic field which is orthogonal to the bilayer surface. Departing from the energy eigenstates of the effective Hamiltonian, the corresponding coherent states will be constructed. For doing this, first we will determine appropriate creation and annihilation operators in order to subsequently derive the coherent states as eigenstates of the annihilation operator with complex eigenvalue. Then, we will calculate some physical quantities, as the Heisenberg uncertainty relation, the probabilities and current density as well as the mean energy value. Finally, we will explore the time evolution for these states and we will compare it with the corresponding evolution for monolayer graphene coherent states.

[17] 2007.02256

A universal, plug-and-play synchronisation scheme for practical quantum networks

We propose and experimentally demonstrate a plug-and-play, practical, and enabling method allowing to synchronize the building blocks of a quantum network in an all-optical way. Our scheme relies on mature and reliable classical telecommunication and non-linear optical technologies and can be implemented in a universal way with off-the-shelf components. Compared to already reported solutions, it allows achieving high-quality synchronization compatible with high network-operation rate and is free from opto-electronic jitters affecting servo-loop based configurations. We test our scheme with a genuine quantum optical method in terms of the interference between two photons coming from two remotely synchronized sources spaced by distances of up to 100 km. Measured visibilities well above 90% confirm the validity of our approach. Due its simplicity and high-quality performance, our scheme paves the way for the synchronization of long-distance quantum networks based on fibre, free-space, as well as hybrid solutions.

[18] 2007.02303

Exact and efficient quantum simulation of open quantum dynamics for various of Hamiltonians and spectral densities

Recently, we have theoretically proposed and experimentally demonstrated an exact and efficient quantum simulation of photosynthetic light harvesting in nuclear magnetic resonance (NMR), cf. B. X. Wang, \textit{et al.} npj Quantum Inf.~\textbf{4}, 52 (2018). In this paper, we apply this approach to simulate the open quantum dynamics in various photosynthetic systems with different Hamiltonians. By numerical simulations, we show that for Drude-Lorentz spectral density the dimerized geometries with strong couplings within the donor and acceptor clusters respectively exhibit significantly-improved efficiency. Based on the optimal geometry, we also demonstrate that the overall energy transfer can be further optimized when the energy gap between the donor and acceptor clusters matches the peak of the spectral density. Moreover, by exploring the quantum dynamics for different types of spectral densities, e.g. Ohmic, sub-Ohmic, and super-Ohmic spectral densities, we show that our approach can be generalized to effectively simulate open quantum dynamics for various Hamiltonians and spectral densities. Because $\log_{2}N$ qubits are required for quantum simulation of an $N$-dimensional quantum system, this quantum simulation approach can greatly reduce the computational complexity compared with popular numerically-exact methods.

[19] 2007.02340

The structure of general quantum Gaussian observable

The structure theorem is established which shows that an arbitrary multi-mode bosonic Gaussian observable can be represented as a combination of four basic cases, the physical prototypes of which are homodyne and heterodyne, noiseless or noisy, measurements in quantum optics. The proof establishes connection between the description of Gaussian observable in terms of the characteristic function and in terms of density of the probability operator-valued measure (POVM) and has remarkable parallels with treatment of bosonic Gaussian channels in terms of their Choi-Jamiolkowski form. Along the way we give the ``most economical'', in the sense of minimal dimensions of the quantum ancilla, construction of the Naimark extension of a general Gaussian observable. It is also shown that the Gaussian POVM has bounded operator-valued density with respect to the Lebesgue measure if and only if its noise covariance matrix is nondegenerate.

[20] 2007.02385

Interference-based universal decoupling and swapping for multimode bosonic systems

A key requirement for bosonic quantum information processing is the ability to control interactions between desired modes of the system. In practical devices, however, this is often difficult to realize due to the presence of undesired coupling to additional modes. In this work, we develop interference-based protocols for decoupling and swapping selected modes of a multimode bosonic system. Specifically, for a generic coupler characterized by Gaussian unitary process, we show how to decouple a single mode or swap any pair of modes with a constant depth sequence of operations, while maintaining the coupling for the remaining system. These protocols require only multiple uses of the same coupler interleaved with single-mode Gaussian unitary operations, and thus enable efficient construction of operations crucial to quantum information science, such as high-fidelity quantum transduction. Our results are directly derived from fundamental physical properties of bosonic systems and are therefore broadly applicable to various existing platforms.

[21] 2007.02483

Star product representation of coherent state path integrals

In this paper, we determine the star product representation of coherent path integrals. By employing the properties of generalized delta functions with complex arguments, the Glauber-Sudarshan P-function corresponding to a non-diagonal density operator is obtained. Then, we compute the Husimi-Kano Q-representation of the time evolution operator in terms of the normal star product. Finally, the optical equivalence theorem allows us to express the coherent state path integral as a star exponential of the Hamiltonian function for the normal product.

[22] 2007.02490

Constructing three-qubit unitary gates in terms of Schmidt rank and CNOT gates

It is known that every two-qubit unitary operation has Schmidt rank one, two or four, and the construction of three-qubit unitary gates in terms of Schmidt rank remains an open problem. We explicitly construct the gates of Schmidt rank from one to seven. It turns out that the three-qubit Toffoli and Fredkin gate respectively have Schmidt rank two and four. As an application, we implement the gates using quantum circuits of CNOT gates and local Hadamard and flip gates. In particular, the collective use of three CNOT gates can generate a three-qubit unitary gate of Schmidt rank seven in terms of the known Strassen tensor from multiplicative complexity. Our results imply the connection between the number of CNOT gates for implementing multiqubit gates and their Schmidt rank.

[23] 2007.02537

Experimental Learning of Pure Quantum States using Sequential Single-Shot Measurement Outcomes

We experimentally implement a machine-learning method for accurately identifying unknown pure quantum states. The method, called single-shot measurement learning, achieves the theoretical optimal accuracy for $\epsilon = O(N^{-1})$ in state learning and reproduction, where $\epsilon$ and $N$ denote the infidelity and number of state copies, without employing computationally demanding tomographic methods. This merit results from the inclusion of weighted randomness in the learning rule governing the exploration of diverse learning routes. We experimentally verify the advantages of our scheme by using a linear-optics setup to prepare and measure single-photon polarization qubits. The experimental results show highly accurate state learning and reproduction exhibiting infidelity of $O(N^{-0.983})$ down to $10^{-5}$, without estimation of the experimental parameters.

[24] 2007.02586

Two-photon phase-sensing with single-photon detection

Path-entangled multi-photon states allow optical phase-sensing beyond the shot-noise limit, provided that an efficient parity measurement can be implemented. Realising this experimentally is technologically demanding, as it requires coincident single-photon detection proportional to the number of photons involved, which represents a severe challenge for achieving a practical quantum advantage over classical methods. Here, we exploit advanced quantum state engineering based on superposing two photon-pair creation events to realise a new approach that bypasses this issue. In particular, optical phase shifts are probed with a two-photon quantum state whose information is subsequently effectively transferred to a single-photon state. Notably, without any multiphoton detection, we infer phase shifts by measuring the average intensity of the single-photon beam on a photodiode, in analogy to standard classical measurements. Importantly, our approach maintains the quantum advantage: twice as many interference fringes are observed for the same phase shift, corresponding to N=2 path-entangled photons. Our results demonstrate that the advantages of quantum-enhanced phase-sensing can be fully exploited in standard intensity measurements, paving the way towards resource-efficient and practical quantum optical metrology.

[25] 2007.02634

On quantum bound states in equiperiodic multi-well potentials I: $-$ Locally periodic potential sequences and Floquet/Bloch bands

Two connected equiperiodic one-dimensional multi-well potentials of different well depths are studied. Floquet/Bloch energy bands for respective multi-well potential are found to be relevant for understanding level structures. Althoug energies are classically allowed in both multi-well potentials, a band gap of one multi-well potential makes this potential quantum-mechanically 'forbidden'. All energy levels are located in the union of the band regions.

[26] 2007.02635

Atomic Raman scattering: Third-order diffraction in a double geometry

In a retroreflective scheme atomic Raman diffraction adopts some of the properties of Bragg diffraction due to additional couplings to off-resonant momenta. As a consequence, double Raman diffraction has to be performed in a Bragg-type regime. Taking advantage of this regime, double Raman allows for resonant higher-order diffraction. We study theoretically the case of third-order diffraction and compare it to first order as well as a sequence of first-order pulses giving rise to the same momentum transfer as the third-order pulse. In fact, third-order diffraction constitutes a competitive tool for the diffraction of ultracold atoms and interferometry based on large momentum transfer since it allows to reduce the complexity of the experiment as well as the total duration of the diffraction process compared to a sequence.

[27] 2007.02656

Qubit-environment entanglement generation and the spin echo

We analyze the relationship between qubit-environment entanglement that can be created during the pure dephasing of the qubit initialized in a superposition of its pointer states, and the effectiveness of the spin echo protocol. Commonly encountered intuitions connecting the amount of decoherence with the amount of qubit-environment entanglement - suggesting that large echo signal corresponds to undoing of a large amount of entanglement - hold only for pure initial states of the environment, which is obviously a rarely encountered case, and we focus here on mixed states of the environment. We show that while the echo protocol can obviously counteract classical environmental noise (but it does not have to, if the noise is not mostly of low-frequency character), it can also undo dephasing associated with qubit-environment entanglement, and there is no obvious difference in its efficiency in these two cases. Additionally, we show that qubit-environment entanglement can be generated at the end of the echo protocol even when it is absent at the time of application of the local operation on the qubit (the $\pi$ pulse). We prove that this can occur only at isolated points in time, after fine-tuning of the echo protocol duration. Finally, we discuss the conditions under which the observation of specific features of the echo signal can serve as a witness of the entangling nature of the joint qubit-environment evolution.

[28] 2007.02682

A switching approach for perfect state transfer over a scalable and routing enabled network architecture with superconducting qubits

We propose a hypercube switching architecture for the perfect state transfer (PST) where we prove that it is always possible to find an induced hypercube in any given hypercube of any dimension such that PST can be performed between any two given vertices of the original hypercube. We then generalise this switching scheme over arbitrary number of qubits where also this routing feature of PST between any two vertices is possible. It is shown that this is optimal and scalable architecture for quantum computing with the feature of routing. This allows for a scalable and growing network of qubits. We demonstrate this switching scheme to be experimentally realizable using superconducting transmon qubits with tunable couplings. We also propose a PST assisted quantum computing model where we show the computational advantage of using PST against the conventional resource expensive quantum swap gates. In addition, we present the numerical study of signed graphs under Corona product of graphs and show few examples where PST is established, in contrast to pre-existing results in the literature for disproof of PST under Corona product. We also report an error in pre-existing research for qudit state transfer over Bosonic Hamiltonian where unitarity is violated.

[29] 2007.02717

Joint separable numerical range and bipartite entanglement witness

In 2017 an idea considering a pair of Hermitian operators of product form was published, which is called ultrafine entanglement witnessing. In 2018 some rigorous results were given. Here we improve their work. First we point this idea can be directly derived from an earlier concept named joint separable numerical range and explain how it works as a series of witnesses. Second by a simple method we present a sufficient condition for an effective pair. Finally we prove this condition is necessary for optimization.

[30] 2007.02718

Genuine high-dimensional quantum steering

High-dimensional quantum entanglement can give rise to stronger forms of nonlocal correlations compared to qubit systems. Beyond being of fundamental interest, this offers significant advantages for quantum information processing. The problem of certifying these stronger correlations, however, remains an important challenge, in particular in an experimental setting. Here we theoretically formalise and experimentally demonstrate a notion of genuine high-dimensional quantum nonlocal steering. We show that high-dimensional entanglement combined with judiciously chosen local measurements can lead to a stronger form of steering, provably impossible to obtain via entanglement in lower dimensions. Exploiting the connection between steering and incompatibility of quantum measurements, we derive simple two-setting steering inequalities for certifying the presence of genuine high-dimensional steering. We report the experimental violation of these inequalities using macro-pixel photon-pair entanglement certifying genuine high-dimensional steering in dimensions up to $d=15$. Our work paves the way for the characterisation and certification of quantum nonlocal correlations in high-dimensional systems.

[31] 2007.02737

Information Geometric Aspects of Probability Paths with Minimum Entropy Production for Quantum State Evolution

We present an information geometric analysis of both entropic speeds and entropy production rates arising from geodesic evolution on manifolds parametrized by pure quantum states. In particular, we employ pure states that emerge as outputs of suitably chosen su(2; C) time-dependent Hamiltonian operators that characterize analog quantum search algorithms of specific types. The su(2; C) Hamiltonian models under consideration are specified by external time-dependent magnetic fields within which spin-1/2 test particles are immersed. The positive definite Riemannian metrization of the parameter manifold is furnished by the Fisher information function. The Fisher information function is evaluated along parametrized squared probability amplitudes obtained from the temporal evolution of these spin-1/2 test particles. A minimum action approach is then utilized to induce the transfer of the quantum system from its initial state to its final state on the parameter manifold over a finite temporal interval. We demonstrate in an explicit manner that the minimal (that is, optimum) path corresponds to the shortest (that is, geodesic) path between the initial and final states. Furthermore, we show that the minimal path serves also to minimize the total entropy production occurring during the transfer of states. Finally, upon evaluating the entropic speed as well as the total entropy production along optimal transfer paths within several scenarios of physical interest in analog quantum searching algorithms, we demonstrate in a transparent quantitative manner a correspondence between a faster transfer and a higher rate of entropy production. We therefore conclude that higher entropic speed is associated with lower entropic efficiency within the context of quantum state transfer.

[32] 2007.02769

Practical security analysis of continuous-variable quantum random number generator with noisy local oscillator

Quantum random number generator (QRNG) can theoretically generate unpredictable random numbers with perfect devices, which is an ideal and secure source of random numbers for cryptography. However, the practical implementations always contain imperfections, which will greatly influence the randomness of the final output and even open loophole to eavesdroppers. Recently, J. Thewes experimentally demonstrate a continuous-variable eavesdropping attack, based on heterodyne detection, on a trusted continuous-variable QRNG in Phys. Rev. A 100, 052318 (2019), yet like many other practical continuous-variable QRNG researches, they always suppose the local oscillator is stable and ignore its fluctuation which might lead to security threats such as wavelength attack. In this work, based on the theory of the conditional min-entropy, imperfections on the practical security of continuous-variable QRNG are systematically analyzed, especially the local oscillator fluctuation under imbalanced homodyne detection. Experiments of a practical QRNG based on vacuum fluctuation are demonstrated to show the influence of local oscillator fluctuation on the total measurement noise variances and the practical conditional min-entropy with beam splitters of different transmittances. Moreover, a local oscillator monitoring method is proposed for the practical continuous-variable QRNG, which can be used to calibrate the practical conditional min-entropy.

[33] 2007.02782

Synchronous linear constraint system games

Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of perfect strategies. They are called the game algebra and the solution group. Here we show that these objects are essentially the same, i.e., that the game algebra is a suitable quotient of the group algebra of the solution group. We also demonstrate that linear constraint system games are equivalent to graph isomorphism games on a pair of graphs parameterized by the linear system.

[34] 2007.02788

Quantum speed limit for robust state characterization and engineering

In this paper, we propose a concept to use a quantum speed limit (QSL) as a measure of robustness of states, defining that a state with bigger QSL is more robust. In this perspective, it is important to have an explicitly-computable QSL, because then we can formulate an engineering problem of Hamiltonian that makes a target state robust against decoherence. Hence we derive a new explicitly-computable QSL that is applicable to general Markovian open quantum systems. This QSL is tighter than another explicitly-computable QSL, in an important setup such that decoherence is small. Also the Hamiltonian engineering problem with this QSL is a quadratic convex optimization problem, and thus it is efficiently solvable. The idea of robust state characterization and the Hamiltonian engineering, in terms of QSL, is demonstrated with several examples.

[35] 2007.02796

Phase tracking for sub-shot-noise-limited receivers

Non-conventional receivers for phase-coherent states based on non-Gaussian measurements such as photon counting surpass the sensitivity limits of shot-noise-limited coherent receivers, the quantum noise limit (QNL). These non-Gaussian receivers can have a significant impact in future coherent communication technologies. However, random phase changes in realistic communication channels, such as optical fibers, present serious challenges for extracting the information encoded in coherent states. While there are methods for correcting random phase noise with conventional heterodyne detection, phase-tracking for non-Gaussian receivers surpassing the QNL is still an open problem. Here we demonstrate phase tracking for non-Gaussian receivers to correct for time-varying phase noise while allowing for decoding beyond the QNL. The phase-tracking method performs real-time parameter estimation and correction of phase drifts using the data from the non-Gaussian discrimination measurement, without relying on phase reference pilot fields. This method enables non-Gaussian receivers to achieve higher sensitivities and rates of information transfer than ideal coherent receivers in realistic channels with time-varying phase noise. This demonstration makes sub-QNL receivers a more robust, feasible, and practical quantum technology for classical and quantum communications.

[36] 2007.02866

Ancilla mediated qubit readout and heralded entanglement between rare-earth dopant ions in crystals

Owing to their long excited state lifetimes, rare-earth ions in crystals are widely used in quantum applications. To allow optical readout of the qubit state of individual ions, we propose to dope the crystal with an additional nearby ancilla ion with a shorter radiative lifetime. We show how a Bayesian analysis exhausts the information about the state of the qubit from the optical signal of the ancilla ion. We study the effects of incoherent processes and propose ways to reduce their effect on the readout. Finally, we extend the architecture to ions residing in two remote cavities, and we show how continuous monitoring of fluorescence signals from the two ancilla ions leads to entanglement of the qubit ions.

[37] 2007.02870

Non-Markovianity of Quantum Brownian Motion

We study quantum non-Markovian dynamics of the Caldeira-Leggett model, a prototypical model for quantum Brownian motion describing a harmonic oscillator linearly coupled to a reservoir of harmonic oscillators. Employing the exact analytical solution of this model one can determine the size of memory effects for arbitrary couplings, temperatures and frequency cutoffs. Here, quantum non-Markovianity is defined in terms of the flow of information between the open system and its environment, which is quantified through the Bures metric as distance measure for quantum states. This approach allows us to discuss quantum memory effects in the whole range from weak to strong dissipation for arbitrary Gaussian initial states. A comparison of our results with the corresponding results for the spin-boson problem show a remarkable similarity in the structure of non-Markovian behavior of the two paradigmatic models.

[38] 2007.02872

Quantum coherence and speed limit in the mean-field Dicke model of superradiance

Dicke superrandiance is a cooperative phenomenon which arises from the collective coupling of an ensemble of atoms to the electromagnetic radiation. Here we discuss the quantifying of quantum coherence for the Dicke model of superradiance in the mean-field approximation. We found the single-atom $l_1$-norm of coherence is proportional to the square root of the average intensity of radiation emitted by the superradiant system, thus showing that quantum coherence stands as a crucial figure of merit towards to the understanding of superradiance phenomenon in the mean-field approach. Furthermore, given the nonlinear unitary dynamics of the time-dependent single-atom state that effectively describes the system of $N$ atoms, we analyze the quantum speed limit time and its interplay with the $l_1$-norm of coherence. We verify the quantum coherence speeds up the evolution of the superradiant system, i.e., the more coherence stored on the single-atom state, the faster the evolution. These findings unveil the role played by quantum coherence in superradiant systems, which in turn could be of interest in condensed matter physics and quantum optics platforms.

[39] 2007.02882

Graph approach to quantum teleportation dynamics

Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations aimed at allowing us a better understanding of the physics involved in the process from different perspectives. With this purpose, here an approach based on graph theory is introduced and discussed in the context of some applications. Its main goal is to provide a fully symbolic framework for quantum teleportation from a dynamical viewpoint, which makes explicit at each stage of the process how entanglement and information swap among the qubits involved in it. In order to construct this dynamical perspective, it has been necessary to define some auxiliary elements, namely virtual nodes and edges, as well as an additional notation for nodes describing potential states (against nodes accounting for actual states). With these elements, not only the flow of the process can be followed step by step, but they allow us to establish a direct correspondence between this graph-based approach and the usual state vector description. To show the suitability and versatility of this graph-based approach, several particular teleportation examples are examined, which include bipartite, tripartite and tetrapartite maximally entangled states as quantum channels. From the analysis of these cases, a general protocol is discussed in the case of sharing a maximally entangled multi-qubit system.

[40] 2007.02885

Converting translation operators into plane polar and spherical coordinates and their use in determining quantum-mechanical wavefunctions in a representation-independent fashion

Quantum mechanics is often developed in the position representation, but this is not necessary, and one can perform calculations in a representation-independent fashion, even for wavefunctions. In this work, we illustrate how one can determine wavefunctions, aside from normalization, using only operators and how those operators act on state vectors. To do this in plane polar and spherical coordinates requires one to convert the translation operator into those coordinates. As examples of this approach, we illustrate the solution of the Coulomb problem in two and three dimensions without needing to express any operators in position space.

[41] 2007.02925

Reducing unitary and spectator errors in cross resonance with optimized rotary echoes

We present an improvement to the cross resonance gate realized with the addition of resonant, target rotary pulses. These pulses, applied directly to the target qubit, are simultaneous to and in phase with the echoed cross resonance pulses. Using specialized Hamiltonian error amplifying tomography, we confirm a reduction of error terms with target rotary -- directly translating to improved two-qubit gate fidelity. Beyond improvement in the control-target subspace, the target rotary reduces entanglement between target and target spectators caused by residual quantum interactions. We further characterize multi-qubit performance improvement enabled by target rotary pulsing using unitarity benchmarking and quantum volume measurements, achieving a new record quantum volume for a superconducting qubit system.

[42] 2007.02057

Experimental evidence for topological phases in the magnetoconductance of 2DEG-based hybrid junctions

Several theoretical studies have recently predicted that the Majorana phases could be realized as quantized plateaus in the magnetoconductance of the artificially engineered hybrid junctions based on two-dimensional electron gases (2DEG) under fully out-of-plane magnetic fields. The large transverse Rashba spin-orbit interaction in 2DEG together with a strong orbital effect due to magnetic fields yield topological phase transitions to nontrivial phases hosting Majorana modes. Such Majorana modes are formed at the ends of 2DEG-based wires with a hybrid superconductor-semiconductor integrity. Here, we report on the experimental observation of such topological phases in hybrid junctions on an In0.75Ga0.25As 2DEG platform by sweeping small out-of-plane magnetic fields (B< 100 mT) and probing the conductance to highlight the characteristic quantized magnetoconductance plateaus. The observed signature of topological phases in small out-of-plane magnetic fields in planar hybrid junctions suggests that In0.75Ga0.25As heterostructure affords a promising material platform for the realization of scalable topological circuits for the applications in quantum technologies.

[43] 2007.02071

Waveguide quantum optomechanics: parity-time phase transitions in ultrastrong coupling regime

We develop a rigorous theoretical framework for interaction-induced phenomena in the waveguide quantum electrodynamics (QED) driven by mechanical oscillations of the qubits. Specifically, we predict that the simplest set-up of two qubits, harmonically trapped over an optical waveguide, enables the ultrastrong coupling regime of the quantum optomechanical interaction. Moreover, the combination of the inherent open nature of the system and the strong optomechanical coupling leads to emerging parity-time (\PT) symmetry, quite unexpected for a purely quantum system without artificially engineered gain and loss. The $\mathcal{PT}$ phase transition drives long-living subradiant states, observable in the state-of-the-art waveguide QED setups.

[44] 2007.02093

Tensor monopoles and negative magnetoresistance effect in four-dimensional optical lattices

We propose that a kind of four-dimensional (4D) Hamiltonians, which host tensor monopoles related to quantum metric tensor in even dimensions, can be simulated by ultracold atoms in the optical lattices. The topological properties and bulk-boundary correspondence of tensor monopoles are investigated in detail. By fixing the momentum along one of the dimensions, it can be reduced to an effective three-dimensional model manifesting with a nontrivial chiral insulator phase. Using the semiclassical Boltzmann equation, we calculate the longitudinal resistance against the magnetic field $B$ and find a negative relative magnetoresistance effect of approximately $ -B^{2} $ dependence when a hyperplane is cut through the tensor monopoles in the parameter space. We also propose an experimental scheme to realize this 4D Hamiltonian by extending an artificial dimension in 3D optical lattices. Moreover, we show that the quantum metric tensor can be detected by applying an external drive in the optical lattices.

[45] 2007.02138

Electronic Properties of Graphene Quantum Ring with Wedge Disclination

We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry of radius $R$ and width $w$ subjected to a magnetic flux. We consider the case where the crystal symmetry is locally modified by replacing a hexagon by a pentagon, square, heptagon or octagon. To model this type of defect we include appropriate boundary conditions for the angular coordinate. The electrons are confined to a finite width strip in radial direction by setting infinite mass boundary conditions at the edges of the strip. The solutions are expressed in terms of Hankel functions and their asymptotic behavior allows to derive quantized energy levels in the presence of an energy gap. We also investigate the persistent currents that appear in the quantum ring and how wedge disclination influences different quantum transport quantities.

[46] 2007.02166

Induced interactions and quench dynamics of bosonic impurities immersed in a Fermi sea

We unravel the ground state properties and the non-equilibrium quantum dynamics of two bosonic impurities immersed in an one-dimensional fermionic environment by applying a quench of the impurity-medium interaction strength. In the ground state, the impurities and the Fermi sea are phase-separated for strong impurity-medium repulsions while they experience a localization tendency around the trap center for large attractions. We demonstrate the presence of attractive induced interactions mediated by the host for impurity-medium couplings of either sign and analyze the competition between induced and direct interactions. Following a quench to repulsive interactions triggers a breathing motion in both components, with an interaction dependent frequency and amplitude for the impurities, and a dynamical phase-separation between the impurities and their surrounding for strong repulsions. For attractive post-quench couplings a beating pattern owing its existence to the dominant role of induced interactions takes place with both components showing a localization trend around the trap center. In both quench scenarios, attractive induced correlations are manifested between non-interacting impurities and are found to dominate the direct ones only for quenches to attractive couplings.

[47] 2007.02312

Clarifying multiple-tip effects on Scanning Tunneling Microscopy imaging of 2D periodic objects and crystallographic averaging in the spatial frequency domain

Crystallographic image processing (CIP) techniques may be utilized in scanning probe microscopy (SPM) to glean information that has been obscured by signals from multiple probe tips. This may be of particular importance for scanning tunneling microscopy (STM) and requires images from a sample that is periodic in two dimensions. The image-forming current for multiple tips in STM is derived in a more straightforward manner than prior approaches. The Fourier spectrum of the current for p4mm Bloch surface wave functions and a pair of delta function tips reveals the tip-separation dependence of various types of image obscurations. In particular our analyses predict that quantum interference should be visible on a macroscopic scale in the form of bands quite distinct from the basket-weave patterns a purely classical model would create at the same periodic double STM tip separations. A surface wave function that models the essential character of highly (0001) oriented pyrolytic graphite (technically known as HOPG) is introduced and used for a similar tip-separation analysis. Using a bonding H_2 tip wave function with significant spatial extent instead of this pair of infinitesimal Dirac delta function tips does not affect these outcomes in any observable way. This is explained by Pierre Curie's well known symmetry principle. Classical simulations of multiple tip effects in STM images may be understood as modeling multiple tip effects in images that were recorded with other types of SPMs). Our analysis clarifies why CIP and crystallographic averaging work well in removing the effects of a blunt SPM tip (that consist of multiple mini-tips) from the recorded 2D periodic images and also outlines the limitations of this image processing techniques for certain spatial separations of STM mini-tips.

[48] 2007.02431

A stochastic calculus approach to the oracle separation of BQP and PH

After presentations of Raz and Tal's oracle separation of BQP and PH result, several people (e.g. Ryan O'Donnell, James Lee, Avishay Tal) suggested that the proof may be simplified by stochastic calculus. In this short note, we describe such a simplification.

[49] 2007.02469

Observation of phonon trapping in the continuum with topological charges

Phonon trapping has an immense impact in many areas of science and technology, from the antennas of interferometric gravitational wave detectors to chip-scale quantum micro- and nano-mechanical oscillators. It usually relies on the mechanical suspension--an approach, while isolating selected vibrational modes, leads to serious drawbacks for interrogation of the trapped phonons, including limited heat capacity and excess noises via measurements. To circumvent these constraints, we realize a new paradigm of phonon trapping using mechanical bound states in the continuum (BICs) with topological features and conducted an in-depth characterization of the mechanical losses both at room and cryogenic temperatures. Our findings of mechanical BICs combining the microwave frequency and macroscopic size unveil a unique platform for realizing mechanical oscillators in both classical and quantum regimes. The paradigm of mechanical BICs might lead to unprecedented sensing modalities for applications such as rare-event searches and the exploration of the foundations of quantum mechanics in unreached parameter spaces.

[50] 2007.02521

Combining density based dynamical correlation with a reduced density matrix strong correlation description

A combined density and first-order reduced-density-matrix (1RDM) functional method is proposed for the calculation of potential energy curves (PECs) of molecular multibond dissociation. Its 1RDM functional part, a pair density functional, efficiently approximates the ab initio pair density of the complete active space self-consistent-field (CASSCF) method. The corresponding approximate on top pair density {\Pi} is employed to correct for double counting a correlation functional of density functional theory (DFT). The proposed ELS-DM{\Pi}DFT method with the extended L\"owdin-Shull (ELS) 1RDM functional with dispersion and multibond (DM) corrections augmented with the {\Pi}DFT functional closely reproduces PECs of multibond dissociation in the paradigmatic N_2 , H_2O, and H_2CO molecules calculated with the recently proposed CAS{\Pi}DFT (CASSCF augmented with a {\Pi} based scaled DFT correlation correction) method. Furthermore, with the additional M-correction, ELS-DM{\Pi}DFT+M reproduces well the benchmark PEC of the N_2 molecule by Lie and Clementi.

[51] 2007.02630

Note on a Floquet/Bloch-band fusion phenomenon in scattering by truncated periodic multi-well potentials

A transmission phenomenon for a quantal particle scattered through a multi-well potential in one dimension is observed by means of an amplitude-phase method. The potential model consists of $N$ identical potential cells, each containing a symmetric well. Typical transmission bands contain $N-1$ possible energies of total transmission. It is found that certain band types contain $n$ energies of total transmission. A fusion phenomenon of this type of band with a typical neigboring band is also found. As the transmission gap between them collapse and disappear, a resulting fused single band is seen to contain $2N-1$ energy peaks of total transmission.

[52] 2007.02685

The Scattering of Dirac Spinors in Rotating Spheroids

There are many stars that are rotating spheroids in the Universe, and studying them is of very important significance. Since the times of Newton, many astronomers and physicists have researched gravitational properties of stars by considering the moment equations derived from Eulerian hydrodynamic equations. In this paper we study the scattering of spinors of the Dirac equation, and in particular investigate the scattering issue in the limit case of rotating Maclaurin spheroids. Firstly we give the metric of a rotating ellipsoid star, then write the Dirac equation under this metric, and finally derive the scattering solution to the Dirac equation and establish a relation between differential scattering cross-section, $\sigma$, and stellar matter density, $\mu$. It is found that the sensitivity of $\sigma$ to the change in $\mu$ is proportional to the density $\mu$. Because of weak gravitational field and constant mass density, our results are reasonable. The results can be applied to white dwarfs, main sequence stars, red giants, supergiant stars and so on, as long as their gravitational fields are so weak that they can be treated in the Newtonan approximations, and the fluid is assumed to be incompressible. Notice that we take the star's matter density to be its average density and the star is not taken to be compact. Obviously our results cannot be used to study neutron stars and black holes. In particular, our results are suitable for white dwarfs, which have average densities of about $10^{5}-10^{6}$\,g~cm$^{-3}$, corresponding to a range of mass of about $0.21-0.61 M_{\bigodot}$ and a range of radius of about $6000-10000$\,km.

[53] 2007.02707

Bright single photon sources in lateral silicon carbide light emitting diodes

Single-photon emitting devices have been identified as an important building block for applications in quantum information and quantum communication. They allow to transduce and collect quantum information over a long distance via photons as so called flying qubits. In addition, substrates like silicon carbide provides an excellent material platform for electronic devices. In this work we combine these two features and show that one can drive single photon emitters within a silicon carbide p-i-n-diode. To achieve this, we specifically designed a lateral oriented diode. We find a variety of new color centers emitting non-classical lights in VIS and NIR range. One type of emitter can be electrically excited, demonstrating that silicon carbide can act as an ideal platform for electrically controllable single photon sources.

[54] 2007.02709

Consistent analytical solution for the response of a nanoscale circuit to a mode-locked laser

It is now common practice to solve the Schr\"odinger equation to estimate the tunneling current between two electrodes at specified potentials, or the transmission through a potential barrier by assuming that there is an incident, reflected, and transmitted wave. However, these two approaches may not be appropriate for applications with nanoscale circuits. A new approach is required because the electron man-free path may be as long as 68.2 nm in metals so it is possible that the wavefunction may be coherent throughout a nanoscale circuit. We define several algorithms for determining the eigenvalues with different sets of the circuit parameters, thus demonstrating the existence of consistent solutions for nanoscale circuits. We also present another algorithm that is being applied to determine the full solution for nanoscale circuits. All of this is done using only analytical solutions of the Schr\"odinger equation.

[55] 2007.02858

The quantum kinetic equation and dynamical mass generation in 2+1 Dimensions

In this work, we study the relativistic quantum kinetic equations in 2+1 dimensions from Wigner function formalism by carrying out a systematic semi-classical expansion up to $\hbar$ order. The derived equations allow us to explore interesting transport phenomena in 2+1 dimensions. Within this framework, the parity-odd transport current induced by the external electromagnetic field is self-consistently derived. We also examine the dynamical mass generation by implementing four-fermion interaction with mean-field approximation. In this case, a new kind of transport current is found to be induced by the gradient of the mean-field condensate. Finally, we also utilize this framework to study the dynamical mass generation in an external magnetic field for the 2+1 dimensional system under equilibrium.

[56] 2007.02859

Weight Distribution of Classical Codes Influences Robust Quantum Metrology

Quantum metrology (QM) is expected to be a prominent use-case of quantum technologies. However, noise easily degrades these quantum probe states, and negates the quantum advantage they would have offered in a noiseless setting. Although quantum error correction (QEC) can help tackle noise, fault-tolerant methods are too resource intensive for near-term use. Hence, a strategy for (near-term) robust QM that is easily adaptable to future QEC-based QM is desirable. Here, we propose such an architecture by studying the performance of quantum probe states that are constructed from $[n,k,d]$ binary block codes of minimum distance $d \geq t+1$. Such states can be interpreted as a logical state of a CSS code whose logical $X$ group is defined by the aforesaid binary code. When a constant, $t$, number of qubits of the quantum probe state are erased, using the quantum Fisher information (QFI) we show that the resultant noisy probe can give an estimate of the magnetic field with a precision that scales inversely with the variances of the weight distributions of the corresponding $2^t$ shortened codes. If $C$ is any code concatenated with inner repetition codes of length linear in $n$, a quantum advantage in QM is possible. Hence, given any CSS code of constant length, concatenation with repetition codes of length linear in $n$ is asymptotically optimal for QM with a constant number of erasure errors. We also explicitly construct an observable that when measured on such noisy code-inspired probe states, yields a precision on the magnetic field strength that also exhibits a quantum advantage in the limit of vanishing magnetic field strength. We emphasize that, despite the use of coding-theoretic methods, our results do not involve syndrome measurements or error correction. We complement our results with examples of probe states constructed from Reed-Muller codes.

[57] 2007.02904

On the minmax regret for statistical manifolds: the role of curvature

Model complexity plays an essential role in its selection, namely, by choosing a model that fits the data and is also succinct. Two-part codes and the minimum description length have been successful in delivering procedures to single out the best models, avoiding overfitting. In this work, we pursue this approach and complement it by performing further assumptions in the parameter space. Concretely, we assume that the parameter space is a smooth manifold, and by using tools of Riemannian geometry, we derive a sharper expression than the standard one given by the stochastic complexity, where the scalar curvature of the Fisher information metric plays a dominant role. Furthermore, we derive the minmax regret for general statistical manifolds and apply our results to derive optimal dimensional reduction in the context of principal component analysis.