Measure Of Quantum Correlations Research Articles

Signatures of intrinsic decoherence and weak measurement on quantum correlations

In this article, we consider a pair of spin-1/2 particles with squeezing coupling serving as the physical carrier of quantum information. We then examine the dynamics of quantum correlation quantified by the entanglement and measurement-induced nonlocality (MIN) under the intrinsic decoherence. The impact of intrinsic decoherence on the dynamical behaviors of quantum correlations is investigated. We show that the MIN quantities are more robust, while intrinsic decoherence cause sudden death in entanglement. Besides, we highlight the role of spin squeezing coupling and external magnetic field on quantum correlation measures. Finally, we investigate the impact of weak measurement on MIN.

Asymmetry-induced nonclassical correlation

In quantum resource theory (QRT), asymmetry recognized as a valid resource for the advantage of various quantum information processing. In this paper, we establish the resource theory of asymmetry using quantum Fisher information (QFI). By defining the average Fisher information as a measure of asymmetry, it is shown that the discrepancy of bipartite global and local asymmetries naturally induces the nonclassical correlation between the subsystems. This measure satisfies all the necessary axioms of a faithful measure of bipartite quantum correlation. As an illustration, we have studied the proposed measure for an arbitrary pure state and Bell diagonal state.

Computable Rényi mutual information: Area laws and correlations

The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on Rényi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.

PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY

Considering the quantum memory channels, we study the dynamical evolutions of quantum coherence and quantum mutual information as measures of quantum correlations under the actions of different decoherence channels on some bipartite initial states. Under any quantum operation or process occurring in a noisy environment, quantum correlations exhibit behavior that does not increase due to the system interacting with its environment. We state that for such a case the decrement of quantum correlations can be improved by the suitable choice of the initial states and by adjusting the parameters. Thus quantum correlations can be partially preserved against the action of the environment. It can be shown that optimal conditions to prohibit the partial loss in quantum coherence and quantum mutual information for performing any quantum information task may be generated by the memory.

Local Measurement-Induced Minimal Decoherence and its variants

Based on quantum measurement, the existing quantum correlation (QC) measures are divided into two categories, one class based on minimal entropy-like difference of the measurement fore-and-aft system density matrix, and the other based on minimal trace-like geometric distance of the measurement fore-and-aft system density matrix. Here we provide another class of QC measure, Local Measurement-Induced Minimal Decoherence (LMIMD) which indicates the simple and clear relationship between QC and quantum coherence. Its physical picture is intuitive and clear. These also indicate that the design realization of its experiment detection and specific potential applications with the superiorities would be much easier. In terms of some typical quantum systems, we investigate and analyze the advantages and disadvantages of the LMIMD and its variants Local Eigen-Measurement-Induced Minimal Decoherence (LEMIMD) and Local Eigen-Measurement-Induced Decoherence (LEMID) compared with the existing two classes of QC measure.

Log to log-log crossover of entanglement in a (1+1) -dimensional massive scalar field

We study three different measures of quantum correlations -- entanglement spectrum, entanglement entropy, and logarithmic negativity -- for (1+1)-dimensional massive scalar field in flat spacetime. The entanglement spectrum for the discretized scalar field in the ground state indicates a cross-over in the zero-mode regime, which is further substantiated by an analytical treatment of both entanglement entropy and logarithmic negativity. The exact nature of this cross-over depends on the boundary conditions used -- the leading order term switches from a $\log$ to $\log-\log$ behavior for the Periodic and Neumann boundary conditions. In contrast, for Dirichlet, it is the parameters within the leading $\log-\log$ term that are switched. We show that this cross-over manifests as a change in the behavior of the leading order divergent term for entanglement entropy and logarithmic negativity close to the zero-mode limit. We thus show that the two regimes have fundamentally different information content. Furthermore, an analysis of the ground state fidelity shows us that the region between critical point $\Lambda=0$ and the crossover point is dominated by zero-mode effects, featuring an explicit dependence on the IR cutoff of the system. For the reduced state of a single oscillator, we show that this cross-over occurs in the region $Nam_f\sim \mathscr{O}(1)$.

Measure and control of quantum correlations in optomechanics

Measure and control of quantum correlations in optomechanics

Robustness of Measurement–Induced Correlations Under Decoherence Effect

In this article, we study the dynamics of quantum correlation measures such as entanglement and measurement–induced nonlocality (MIN). Starting from an arbitrary Bell-diagonal mixed state under Markovian local noise such as bit-phase flip, depolarizing and generalized amplitude damping channel, we provide the decays of the entanglement measured by concurrence and quantum correlation captured by different forms of MIN (trace distance, Hilbert–Schmidt norm and relative entropy) as a function of the decoherence parameters. The effect of local noises on the dynamical behaviors of quantum correlation is also observed. We show the existence of specific and important features of MIN such as revival, noise robustness and sudden change with respect to decoherence parameter. It is observed that all the noises cause sudden death of entanglement for partially entangled states. Further, we show the existence of separable quantum states with non-zero quantum correlations in terms of MIN.

Multipartite nonlocality in one-dimensional quantum spin chains at finite temperatures

Multipartite nonlocality is an important measure of multipartite quantum correlations. In this paper, we show that the nonlocal $n$-site Mermin-Klyshko operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}}_{n}$ can be exactly expressed as a matrix product operator with a bond dimension $D=2$, and then the calculation of nonlocality measure $\mathcal{S}$ can be simplified into standard one-dimensional (1D) tensor networks. With the help of this technique, we analyze finite-temperature multipartite nonlocality in several typical 1D spin chains, including an $XX$ model, an $XXZ$ model, and a Kitaev model. For the $XX$ model and the $XXZ$ model, in a finite-temperature region, the logarithm measure of nonlocality (${log}_{2}\mathcal{S}$) is a linear function of the temperature $T$, i.e., ${log}_{2}\mathcal{S}\ensuremath{\sim}\ensuremath{-}aT+b$. It provides us with an intuitive picture about how thermodynamic fluctuations destroy multipartite nonlocality in 1D quantum chains. Moreover, in the $XX$ model $\mathcal{S}$ presents a magnetic-field-induced oscillation at low temperatures. This behavior has a nonlocal nature and cannot be captured by local properties such as the magnetization. Finally, for the Kitaev model, we find that in the limit $T\ensuremath{\rightarrow}0$ and $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the nonlocality measure may be used as an alternative order parameter for the topological-type quantum phase transition in the model.

The link between Fisher information and geometric discord

By considering an arbitrary two-qubit state, it is shown that the Fisher information is intrinsically linked to the geometric discord which allows a measure for quantum correlations beyond entanglement. The complex amplitude of oscillations of the probability density function is upper bounded by the geometric discord which subsequently results in the Fisher information being bounded by the geometric discord. This gives an experimental observable which can be used to quantify quantum correlations beyond entanglement. This observable can be used to witness quantum correlations in an interferometry experiment, and provide another avenue for quantum technologies to continue to develop.

Total versus quantum correlations in a two-mode Gaussian state

In Li and Luo (2007 Phys. Rev. A 76 032327), the inequality was identified as a fundamental postulate for a consistent theory of quantum versus classical correlations for arbitrary measures of total and quantum correlations in bipartite quantum states. Besides, Hayden et al (2006 Commun. Math. Phys. 265 95) have conjectured that, in some conditions within systems endowed with infinite-dimensional Hilbert spaces, quantum correlations may dominate not only half of total correlations but total correlations itself. Here, in a two-mode Gaussian state, quantifying and respectively by the quantum mutual information and the entanglement of formation (EoF) , we verify that is always less than when and are defined via the Rényi-2 entropy. While via the von Neumann entropy, may even dominate itself, which partly consolidates the Hayden conjecture, and partly, provides strong evidence hinting that the origin of this counterintuitive behavior should intrinsically be related to the von Neumann entropy by which the EoF is defined, rather than related to the conceptual definition of the EoF . The obtained results show that—in the special case of mixed two-mode Gaussian states—quantum entanglement can be faithfully quantified by the Gaussian Rényi-2 EoF .

New physics effects on quantum coherence in neutrino oscillations

Several measures of quantum correlations such as Leggett–Garg and Bell-type inequalities have been extensively studied in the context of neutrino oscillations. However, these analyses are performed under the assumption of standard model (SM) interactions of neutrinos. In this work, we study new physics effects on \(l_1\)-norm based measure of quantum coherence which quantifies the quantumness embedded in the system and is also intrinsically related to various measures of quantum correlations. Moreover, it is considered to be a resource theoretical tool which can be utilized in quantum algorithms and quantum channel discrimination. The new physics effects are incorporated in a model independent way by using the effective Lagrangian for the neutral current non-standard neutrino interactions (NSI). Bounds on the NSI parameters are extracted from a recent global analysis of oscillation experiments including COHERENT (coherent neutrino-nucleus scattering experiment) data. In the context of upcoming DUNE experimental setup, we find that the most favourable combination of LMA-Light sector of \(\theta _{12}\) (i.e., \(\theta _{12}< 45^{\circ }\)) with normal mass ordering decreases the coherence in the system in comparison to the SM prediction for all values of neutrino energy E and CP violating phase \(\delta \) (except in the narrow region around \(E \sim \) 2 GeV). On the other hand, a large enhancement in the value of coherence parameter in the entire \((E-\delta )\) plane is possible for the dark octant of \(\theta _{12}\) (\(\theta _{12}> 45^{\circ }\)) with inverted ordering. For almost all values of CP violating phase, the enhancement is more protuberant in the region around \(E \sim \) 4 GeV where maximum neutrino flux is expected in the DUNE experiment. Therefore for the normal mass ordering, the SM interaction provides favourable conditions for quantum information tasks while the NSI favours inverted ordering scenario for such tasks.

Imaging three-dimensional single-atom arrays all at once.

Simultaneous imaging of a three-dimensional distribution of point sources is presented. In a two-lens microscope, the point-spreads on the quasi-image plane, which is located between the Fourier and image planes, are spatially distinct, so a set of Fresnel lenslets can perform individual wave-front shaping for axial and lateral rearrangements of the images. In experiments performed with single atoms and holographically programmed lenslets, various three-dimensional arrangements of point sources, including axially aligned atoms, are successfully refocused on the screen, demonstrating the simultaneous and time-efficient detection of the three-dimensional holographic imaging. We expect that non-sequential real-time measurements of three-dimensional point sources shall be in particular useful for quantum correlation measurements and in situ tracking of dynamic particles.

Dynamics of quantum correlation for three qubits in hierarchical environment

Much attention has been paid to the dynamics of quantum correlation in an open quantum system coupled to a single-layered environment for a long time. However, the system can be influenced by the multilayer environment or hierarchical environment in realistic scenarios, which is attracting increasing interest at present. In this context, we explore in this paper the dynamics of quantum correlation for a quantum system consisting of three independent qubits, each being immersed in a single mode lossy cavity which is further connected to another cavity. The influences of cavity-cavity coupling strength &lt;i&gt;Ω&lt;/i&gt; and the decay rate of cavity &lt;i&gt;Γ&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; on the measures of quantum correlation, including negativity, Bell non-locality as well as entanglement witness, are investigated in detail in a strong coupling regime and a weak coupling regime. It is shown that the phenomena of sudden death and sudden birth can happen to both Bell non-locality and entanglement witness. When the decay rate &lt;i&gt;Γ&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; = 0 is given, with the increase of &lt;i&gt;Ω&lt;/i&gt; these measures eventually reach their stationary values over time after a short period of damping oscillations, in which these stationary values will become larger for the larger &lt;i&gt;Ω&lt;/i&gt;. At the same time, the values or the survival times of quantum correlation considered by us in the weak coupling regime are better than in the strong coupling case. In addition, the non-zero &lt;i&gt;Γ&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; has a great negative effect on quantum correlation. Hence, in order to suppress the loss of quantum correlation better, the effective manipulation of quantum weak measurement and measurement reversal operator is considered further. Some interesting results are obtained.

Effects of nonstandard interaction on temporal and spatial correlations in neutrino oscillations

Effects of physics beyond the standard model in the neutrino sector are conveniently incorporated through non-standard interaction parameters. Assuming new physics in the form of dimension-6 vector operators, a recent global analysis of neutrino oscillation data including results from COHERENT experiment suggests two favourable new physics scenarios. These are LMA-Light (with normal mass ordering) and LMA-Dark (with inverted mass ordering) sectors of parameters. In this work, we study the effects of new physics solutions on Leggett–Garg-type (LGtI) inequality which quantifies temporal correlations in the system along with flavour entropy and genuine tripartite entanglement which can be considered as measures of spatial correlations. We show that the violation of LGtI for nu _{mu } energy around 3 GeV in the DUNE experimental set-up can not only be an indication of presence of new physics but such a new physics is expected to be in the form of LMA-Dark sector with inverted ordering. Further, we show that the LMA-Light solution, in general, decreases the values of all measures of quantum correlations in comparison to their SM predictions. On the other hand, the Dark solution can significantly enhance the values of these measures.

Classical-Noise-Free Sensing Based on Quantum Correlation Measurement* *Supported by Hong Kong RGC/GRF Project (Grant No. 14300119).

Quantum sensing, using quantum properties of sensors, can enhance resolution, precision, and sensitivity of imaging, spectroscopy, and detection. An intriguing question is: Can the quantum nature (quantumness) of sensors and targets be exploited to enable schemes that are not possible for classical probes or classical targets? Here we show that measurement of the quantum correlations of a quantum target indeed allows for sensing schemes that have no classical counterparts. As a concrete example, in the case that the second-order classical correlation of a quantum target could be totally concealed by non-stationary classical noise, the higher-order quantum correlations can single out a quantum target from the classical noise background, regardless of the spectrum, statistics, or intensity of the noise. Hence a classical-noise-free sensing scheme is proposed. This finding suggests that the quantumness of sensors and targets is still to be explored to realize the full potential of quantum sensing. New opportunities include sensitivity beyond classical approaches, non-classical correlations as a new approach to quantum many-body physics, loophole-free tests of the quantum foundation, et cetera.

Steady-state quantum correlation measurement in hybrid optomechanical systems

In this paper, we investigate the steady-state of quantum correlation measurement of hybrid optomechanical systems. The first system consists of a single optomechanical system simultaneously coupled to a mechanical oscillator. While the second system is a hybrid optomechanical system consisting of an atomic ensemble placed in between the optical cavity and mirror. For both optomechanical systems, we formulate the Hamiltonian and the explicit expression of the covariance matrix leading to the dynamic of the system. Under the linearization approximation, we investigate the steady-state quantum correlations which are quantified through the correlation function of non-Hermitian operators, while the logarithmic negativity is used to quantify the amount of quantum entanglement between the subsystems. Furthermore, our proposed quantum correlation function can be used to quantify the entangled bipartite states that are correlative and transfer information. It is found that the transfer of quantum correlations between the subsystem is related to the detuning and coupling strength. Our results provide a realistic route toward remote quantum entanglement detection and a framework of future realistic fiber-optic quantum network operating applications.

:THE COSMOLOGICAL OTOC: Formulating New Cosmological Micro-Canonical Correlation Functions for Random Chaotic Fluctuations in Out-Of-Equilibrium Quantum Statistical Field Theory

The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, using for the first time the slogan “Cosmology meets Condensed Matter Physics”, we demonstrate a formalism to compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following the canonical quantization technique. In this computation, two dynamical time scales are involved—out of them, at one time scale, the cosmological perturbation variable, and for the other, the canonically conjugate momentum, is defined, which is the strict requirement to define the time scale-separated quantum operators for OTOC and is perfectly consistent with the general definition of OTOC. Most importantly, using the present formalism, not only one can study the quantum correlation during stochastic inflation and reheating, but can also study quantum correlation for any random events in Cosmology. Next, using the late time exponential decay of cosmological OTOC with respect to the dynamical time scale of our universe which is associated with the canonically conjugate momentum operator in this formalism, we study the phenomenon of quantum chaos by computing the expression for the Lyapunov spectrum. Furthermore, using the well known Maldacena Shenker Stanford (MSS) bound on the Lyapunov exponent, λ≤2π/β, we propose a lower bound on the equilibrium temperature, T=1/β, at the very late time scale of the universe. On the other hand, with respect to the other time scale with which the perturbation variable is associated, we find decreasing, but not exponentially decaying, behaviour, which quantifies the random quantum correlation function out-of-equilibrium. We have also studied the classical limit of the OTOC and checked the consistency with the large time limiting behaviour of the correlation. Finally, we prove that the normalized version of OTOC is completely independent of the choice of the preferred definition of the cosmological perturbation variable.

Analogies between the topological insulator phase of 2D Dirac materials and the superradiant phase of atom‐field systems

AbstractA semiclassical phase‐space perspective of band‐ and topological‐insulator regimes of 2D Dirac materials and normal‐ and superradiant phases of atom‐field interacting models is given in terms of delocalization, entropies, and quantum correlation measures. From this point of view, the low‐energy limit of tight‐binding models describing the electronic band structure of topological 2D Dirac materials such as phosphorene and silicene with tunable band gaps share similarities with Rabi‐Dicke and Jaynes‐Cummings atom‐field interaction models, respectively. In particular, the edge state of the 2D Dirac materials in the topological insulator phase exhibits a Schrödinger's cat structure similar to the ground state of two‐level atoms in a cavity interacting with a one‐mode radiation field in the superradiant phase. Delocalization seems to be a common feature of topological insulator and superradiant phases.

One-shot detection limits of quantum illumination with discrete signals

To detect a stealth target, one may directly probe it with a single photon and analyze the reflected signals. The efficiency of such conventional detection scheme can potentially be enhanced by quantum illumination, where entanglement is exploited to break the classical limits. The question is what is the optimal signal state for achieving the detection limit? Here, we address this question in a general discrete model, and derive a complete set of analytic solutions. For one-shot detection, the parameter space can be classified into three distinct regions, in the form of a “phase diagram” for both conventional and quantum illumination. Interestingly, whenever the reflectivity of the target is less than some critical value, all received signals become useless, which is true even if entangled resources are employed. However, there does exist a region where quantum illumination can provide advantages over conventional illumination; there, the optimal signal state is an entangled state with an entanglement spectrum inversely proportional to the spectrum of the environmental noise state and is, surprisingly, independent of the occurrence probability and the reflectivity of the object. The entanglement of the ideal probe state increases with the entropy of the environment; it becomes more entangled as the temperature of the environment increases. Finally, we show that the performance advantage cannot be fully characterized by any measure of quantum correlation, unless the environment is a complete mixed state.