Quantify Quantum Correlations Research Articles

Investigating entangled photons to quantify quantum correlations in dual optomechanical cavities.

Quantum correlations that go beyond quantum entanglement have a significant role in the fields of quantum information processing and quantum computation. In essence, when we describe a quantum system using pure states, quantum entanglement and quantum correlation are essentially indistinguishable. However, this equivalence breaks down when dealing with general mixed states. To contribute to understanding this distinction, we have considered a straightforward model for both generating and measuring these quantum correlations. We focus on two macroscopic mechanical resonators situated in separate Fabry–Perot cavities and coupled through the photon hopping process. Our model allows us to conduct a comprehensive examination and quantification of quantum correlations that extend beyond entanglement between these mechanical modes. Our approach begins with the determination of the global covariance matrix, serving as the foundation for calculating two key metrics: the Entropy of Formation and the Gaussian quantum Discord. These metrics enable us to quantify the extent of quantum entanglement and quantum correlations, respectively. Our analysis, based on these quantifiers, reveals that quantum discord serves as a more appropriate metric for characterizing the quantum correlations between the mechanical modes in an optomechanical quantum system, especially in the presence of robust photon hopping.

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation. Essentially, for quantum systems prepared in pure states, it is difficult to differentiate between quantum entanglement and quantum correlation. Nonetheless, this indistinguishability is no longer holds for mixed states. To contribute to a better understanding of this differentiation, we have explored a simple model for both generating and measuring these quantum correlations. Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities, coupled through the photon hopping process. this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes. The key ingredient in analyzing quantum correlation in this system is the global covariance matrix. It forms the basis for computing two essential metrics: the logarithmic negativity ( ENm ) and the Gaussian interferometric power ( PGm ). These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations, respectively. Our study reveals that the Gaussian interferometric power ( PGm ) proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system, particularly in scenarios featuring resilient photon hopping.

Quantifying quantum correlations beyond entanglement via robust photon hopping in an optomechanical system

Quantum correlations beyond quantum entanglement represent vital resources in quantum information processing as well as in quantum computation. In fact, both quantum entanglement and quantum correlation are the same when the quantum system is described by pure states. However, this is not exactly the case when general mixed states are considered. In order to clarify this, a simple model has been proposed for the production and quantification of these quantum correlations between two mechanical resonators that are macroscopic in two Fabry–Pérot cavities optomechanical coupled by the photon hopping process. In this model, we analyze and investigate the quantification of the quantum correlation beyond the entanglement between the mechanical modes. We determine the global covariance matrix of the model from which we derive the expression of the entropy of formation ([Formula: see text]) as well as the Gaussian quantum discord ([Formula: see text]), which quantify the amount of quantum entanglement and quantum correlations, respectively. The analysis based on these two quantum correlations quantifiers shows that quantum discord is more appropriate to characterize the quantum correlations between the mechanical modes in an optomechanical quantum system in the presence of robust photon hopping.

Quantum correlation swapping between qutrit states

In this study, the qubit quantum correlation swapping (QCS) is generalized to the qutrit case. To be concrete, two qutrit Werner states are taken as the research objects and the complete set of qutrit Bell states are utilized as the intermediate two-qutrit measure to implement QCS. The popular quantum correlation measure, i.e. quantum discord (Ollivier and Zurek 2001 Phys. Rev. Lett. 88 017901), is employed to characterize and quantify quantum correlations in the concerned states. The properties of the variance and threshold of quantum correlations occurring in the swapping process are revealed, and two distinct QCS phenomena are thus observed. Moreover, it is found that the maximal amount of quantum correlations in the final state can not exceed the minimal one of these in the initial states.

Efficient separation of quantum from classical correlations for mixed states with a fixed charge

Entanglement is the key resource for quantum technologies and is at the root of exciting many-body phenomena. However, quantifying the entanglement between two parts of a real-world quantum system is challenging when it interacts with its environment, as the latter mixes cross-boundary classical with quantum correlations. Here, we efficiently quantify quantum correlations in such realistic open systems using the operator space entanglement spectrum of a mixed state. If the system possesses a fixed charge, we show that a subset of the spectral values encode coherence between different cross-boundary charge configurations. The sum over these values, which we call "configuration coherence", can be used as a quantifier for cross-boundary coherence. Crucially, we prove that for purity non-increasing maps, e.g., Lindblad-type evolutions with Hermitian jump operators, the configuration coherence is an entanglement measure. Moreover, it can be efficiently computed using a tensor network representation of the state's density matrix. We showcase the configuration coherence for spinless particles moving on a chain in presence of dephasing. Our approach can quantify coherence and entanglement in a broad range of systems and motivates efficient entanglement detection.

Quantifying quantum correlations in noisy Gaussian channels

The Gaussian states are essential ingredients in many tasks of quantum information processing. The presence of the noises imposes limitations on achieving these quantum protocols. Therefore, examining the evolution of quantum entanglement and quantum correlations under the coherence of Gaussian states in noisy channels is of paramount importance. In this paper, we propose and analyze a scheme that aims to specify and examine the dynamic evolution of the quantum correlations in two-mode Gaussian states submitted to the influence of the Gaussian thermal environment. We describe the time evolution of the quantum correlations in an open system consisting of two coupled bosonic modes embedded in a Gaussian thermal environment. We discuss the influence of the environment in terms of the initial parameters of the input states. The quantum correlations are quantified using Gaussian interferometric power and the Gaussian entanglement of formation. The behavior of these quantum correlations quantifiers is strictly dependent on the parameters of the input states that are employed. We show that the Gaussian interferometric power is a measurement quantifier that can capture the essential quantum correlations beyond quantum entanglement. In addition, we show that the Gaussian interferometric power is less influenced than the Gaussian entanglement of formation.

Quantifying quantum correlations in a double cavity–magnon system

Quantifying quantum correlations in a double cavity–magnon system

Dynamics of Negativity of a Wannier–Stark Many‐Body Localized System Coupled to a Bath

An interacting system subjected to a strong linear potential can host a many‐body localized (MBL) phase when being slightly perturbed. This so‐called Wannier–Stark or “tilted‐field” MBL phase inherits many properties from the well‐investigated disordered MBL phase, and provides an alternative route to experimentally engineer interacting localized systems without quenched disorder. Herein, the dynamics of entanglement in a Wannier–Stark MBL system coupled to a dephasing environment is investigated. As an accessible entanglement proxy, the third Rényi negativity is used, which reduces to the third Rényi entropy in case the system is isolated from the environment. This measure captures the characteristic logarithmic growth of interacting localized phases in the intermediate‐time regime, where the effects of the coupling to the environment are not yet dominating the dynamics. Thus, it forms a tool to distinguish Wannier–Stark MBL from noninteracting Wannier–Stark localization up to intermediate time‐scales, and to quantify quantum correlations in mixed‐state dynamics.

Quantifying Quantum Correlation of Quasi‐Werner State and Probing Its Suitability for Quantum Teleportation (Ann. Phys. 10/2021)

Quantum Correlations In article number 2100201, Arpita Chatterjee, Kishore Thapliyal, and Anirban Pathak establish the relevance of photon addition in the enhancement of single- and two-mode (bipartite correlations) nonclassical properties and teleportation performance using the Wigner function, entanglement, and discord of the two-mode quasi-Werner state. Efficacy of photon addition in the entanglement distillation is also established.

Quantifying Quantum Correlation of Quasi‐Werner State and Probing Its Suitability for Quantum Teleportation

AbstractThe significance of photon addition in engineering the single‐ and two‐mode (bipartite correlations) nonclassical properties of a quantum state is investigated. Specifically, the behavior of the Wigner function of two quasi‐Werner states constructed by superposing two normalized bipartite m‐photon added coherent states are analyzed. This allows the authors' to quantify the nonclassicality present in the quantum states using Wigner logarithmic negativity (WLN), while quantum correlations are measured using concurrence, entanglement of formation, and quantum discord. The WLN for a two‐mode state corresponds to the sum of the single‐mode nonclassicality and quantum correlations, and both of these are observed to enhance with photon addition manifesting the efficacy of photon addition in the entanglement distillation. Usefulness of photon addition is further established by showing that the performance of the quasi‐Werner states as quantum channel for the teleportation of single‐mode coherent and squeezed states, as quantified via teleportation fidelity, improves with the photon addition. The non‐Gaussian operation is shown effective in stalling the detrimental effects of transmission through noisy channel and/or inefficient detection under realistic scenario. Further, in contrast to a set of existing results, it is established that the negative values of two‐mode Wigner function is not a witness of quantum correlation.

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.

Dynamics of quantum discord based on linear entropy and negativity of qutrit-qubit system under classical dephasing environments

A reliable analytical method to evaluate the non-classical correlations based on linear entropy for an arbitrary qudit-qubit quantum state is proposed. The linear entropy is used to overcome the difficulty encountered with the computability of quantum discord based on von Neumann entropy. The quantum discord based on linear entropy is employed to derive the quantum correlations for a qutrit-qubit system undergoing global (bilocal + collective) classical dephasing environment. Our studies were focused mainly on a particular initial qutrit-qubit state in thermal equilibrium at a temperature T. The obtained amount of quantum discord (QD) is then compared with the measurement-induced disturbance (MID) and logarithmic negativity (LN). The analysis shows that both QD and MID are more robust than entanglement (LN) against the decoherence effect. Besides, the system exhibits interesting behaviors. As for instance, freezing dynamics and entanglement sudden death (ESD). The method developed in this paper to quantify quantum correlations is reliable because it allows us to consider analytically the arbitrary qutrit-qubit quantum states in the classical dephasing environment.

Experimentally Demonstrate the Spin-1 Information Entropic Inequality Based on Simulated Photonic Qutrit States.

Quantum correlations of higher-dimensional systems are an important content of quantum information theory and quantum information application. The quantification of quantum correlation of high-dimensional quantum systems is crucial, but difficult. In this paper, using the second-order nonlinear optical effect and multiphoton interference enhancement effect, we experimentally implement the photonic qutrit states and demonstrate the spin-1 information entropic inequality for the first time to quantitative quantum correlation. Our work shows that information entropy is an important way to quantify quantum correlation and quantum information processing.

The pairwise quantum correlations for teleported state via a symmetric multi-qubit system

We study the pairwise quantum correlations for teleported state via a symmetric multi-qubitsystem. In the other words, the proposed model is considered as a quantum channel. Using thequantum discord, super quantum discord and concurrence to quantify quantum correlations forteleported state, some analytical and numerical results are presented. Moreover, we compare thedynamical evolutions of quantum correlations and fidelity versus measurement strength and thenumber of qubit channel for teleported state via symmetric multi-qubit model. Our main goalnow is to study how we can increase the quantum correlations and the fidelity of the teleportedstate in the presence of decoherence. The results show that, measurement strength and thenumber of qubit can control the quantum information obtained through the quantum channel.Therefore, measurement strength can be a good option for measuring exchanged information inthe teleportation process. In addition to, quantum correlations can provide an effective role inquantum teleportation

Non-equilibrium absorbing state phase transitions in discrete-time quantum cellular automaton dynamics on spin lattices

We introduce a discrete-time quantum dynamics on a two-dimensional lattice that describes the evolution of a 1 + 1-dimensional spin system. The underlying quantum map is constructed such that the reduced state at each time step is separable. We show that for long times this state becomes stationary and displays a continuous phase transition in the density of excited spins. This phenomenon can be understood through a connection to the so-called Domany–Kinzel automaton, which implements a classical non-equilibrium process that features a transition to an absorbing state. Near the transition density–density correlations become long-ranged, and interestingly the same is the case for quantum correlations despite the separability of the stationary state. We quantify quantum correlations through the local quantum uncertainty and show that in some cases they may be determined experimentally solely by measuring expectation values of classical observables. This work is inspired by recent experimental progress in the realization of Rydberg lattice quantum simulators, which—in a rather natural way—permit the realization of conditional quantum gates underlying the discrete-time dynamics discussed here.

Entanglement, EPR steering and Gaussian geometric discord in a double cavity optomechanical systems

The aim of the present paper is the quantification of non-classical correlations between mechanical and optical modes in an optomechanical system with two spatially separated Fabry-Perot cavities, using resolver sideband regime. To measure the amount of stationary entanglement, we use the criterion of Reid et al, while the evolution of the Gaussian quantum steering and its asymmetry make it possible to study the steerability of the correlations transfer between the different modes. Then, a theoretical study of the robustness of the Gaussian geometric discord (GGD), with respect to the temperature of the environment, is realized, for the two-mode symmetrical squeezed thermal states, to quantify quantum correlations beyond entanglement between mechanical and optical modes. By considering recent experimental parameters, we show that GGD is more robust than entanglement for a high thermal bath temperature. Finally, we find that these three indicators of quantumness enhance with the increase of the squeezing parameter.

Quantifying quantum correlation via quantum coherence

Resource theory is applied to quantify the quantum correlation of a bipartite state and a computable measure is proposed. Since this measure is based on quantum coherence, we present another possible physical meaning for quantum correlation, i.e., the minimum quantum coherence achieved under local unitary transformations. This measure satisfies the basic requirements for quantifying quantum correlation and coincides with concurrence for pure states. Since no optimization is involved in the final definition, this measure is easy to compute irrespective of the Hilbert space dimension of the bipartite state.

Problem of quantifying quantum correlations with non-commutative discord

In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Y. Guo [Sci. Rep. 6, 25241 (2016)]. By recourse to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt's is used. In order to avoid this dependence on the basis, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt's. In addition, the resulting measure inherits the main properties of Guo's measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such a optimization. The results show that, in most cases of interest, the use of Guo's measure can result in a overestimation of quantum correlations. However, since Guo's measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.

Role of Wigner function in studying quantum correlations

In this paper, we investigate the possibility to use the Wigner function to detect and quantify quantum correlations in general. We study these quantum correlations for two quasi-Werner states formed with two general bipartite superposed squeezed states. We find then that the Wigner function is not sensitive to all kinds of quantum correlations but it only witnesses entanglement.

Pairwise Quantum Discord for a Symmetric Multi-Qubit System in Different Types of Noisy Channels

We study the pairwise quantum discord (QD) for a symmetric multi-qubit system in different types of noisy channels, such as phase-flip, amplitude damping, phase-damping, and depolarizing channels. Using the QD and geometric measure of quantum discord (GMQD) to quantify quantum correlations, some analytical or numerical results are presented. The results show that, the dynamics of the pairwise QD is related to the number of spin particles $N$ as well as initial parameter $\theta$ of the one-axis twisting collective state. With the number of spin particles $N$ increasing, the amount of the pairwise QD increases. However, when the amount of the pairwise QD arrives at a stable maximal value, the pairwise QD is independence of the number of spin particles $N$ increasing. The behavior of the pairwise QD is symmetrical during a period $0\leq \theta \leq 2\pi$. Moreover, we compare the pairwise QD dynamics with the GMQD for a symmetric multi-qubit system in different types of noisy channels.