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International Journal of Geometric Methods in Modern Physics

Studying quantum correlations dynamics in the phase space for continuous-variable Werner states and Bell-diagonal states

Fatima-Zahra Siyouri, Hicham Ait Mansour, Fadoua Elbarrichi

Published May 3, 2019• 1 citation
Publisher

Abstract

We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.

DOI
10.1142/s0219887819501093

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We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.
We study the dynamics of Wigner function, quantum discord, entanglement and quantum dissonance for bipartite Bell-diagonal states independently interacting with dephasing reservoirs. We analyze comparatively their behavior under the decoherence effect. Our main goal is to test the ability of Wigner function negativity to measure all kinds of quantum correlations in such system. Particularly, we find that this negativity can only capture entanglement and discord. Of course it succeeded in predicting the behavior of quantum dissonance, but nevertheless, it failed to detect its presence. As a matter of fact, we conclude that Wigner function negativity cannot be used as measure of quantum dissonance in the two qubit open system.
The central aim of the thesis is to examine how non-classical resources in finite-dimensional quantum systems can be identified, characterized, and protected for practical use in the presence of realistic noise. Using the discrete Wigner functions (DWFs) framework, we introduce negative quantum states and examine how their Wigner negativity, mana, coherence, and teleportation fidelity evolve under unital and non-unital channels, with particular attention to non-Markovian random-telegraph and amplitude-damping dynamics. We also analyze protection strategies based on weak measurement and quantum measurement reversal, showing that these methods can enhance quantum correlations, reduce fidelity deviation, and improve teleportation performance for two-qubit negative states in memory-bearing environments. Moreover, we demonstrate that certain negative states, derived from phase-space point operators, exhibit greater resilience than Bell states in measures of entanglement under non-Markovian noise. Further, this thesis focuses on developing and implementing quantum circuits for generating these states on superconducting hardware and realizing them for the first time on IBM's ibm-Brisbane device. Their preparation is verified using quantum state tomography, demonstrating high fidelity under realistic noise conditions. We propose a teleportation scheme that leverages one of the two-qubit negative quantum states as a resource. Moreover, these two-qubit negative quantum states are also found to perform better than the Bell states for maximal CHSH violation and Fisher information in noisy conditions. We believe that these negative quantum states have the potential to be used in place of the traditional Bell states in scenarios where non-Markovian errors are prevalent. (continued in the PDF)
Local available quantum correlations (LAQCs), as dened by Mundarain et al. [19], are analytically determined for Bell Diagonal states. Using the Kraus operators formalism [10], we analyze the dissipative dynamics of 2-qubit LAQCs under Markovian decoherence. This is done for Werner states under the depolarizing [20] and phase damping channels [21]. Since Werner states are among those that exhibit the so called entanglement sudden death [27], the results are compared with the ones obtained for Quantum Discord [22], as analyzed by Werlang et al. [24], as well as for entanglement, i.e. Concurrence[7]. The LAQCs quantier, as Quantum Discord does, only vanishes asymptotically.
We investigate the behavior of quantum correlations in some specific Werner-like two-qubit states, where the qubit interacts individually with non-Markovian environment. We employ the local quantum uncertainty and trace distance discord to quantify the amount of quantum correlations between the evolved qubits and the corresponding analytical expressions are derived. For specific values of the parameters characterizing the whole system, the dynamics of quantum correlations exhibits collapse and revival phenomena. The influence of the non-Markovianity is also investigated to analyze the monotonic decay of quantum correlations in the limiting case of Markovian regime. Furthermore, we show that trace distance discord captures quantum correlations that cannot be revealed by local quantum uncertainty in some particular situations.
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 the proposed 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.