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Entropy

Analytic Expression of Quantum Discords in Werner States under LQCC

Chuanmei Xie, Zhanjun Zhang, Jianlan Chen, Xiaofeng Yin

Published Jan 26, 2020• 5 citations
Publisher

Abstract

In this paper, quantum discords in a special kind of states, i.e., Werner states by local quantum operations and classical communication (LQCC) protocols (WLQCC states), are studied. Nineteen parameters to quantify the quantum discords are reduced to four parameters in terms of properties of Werner states and quantum discord. In the case of orthogonal projective measures, analytic expression of quantum discords in WLQCC states is analytically worked out. Some properties of the quantum discord in the WLQCC states are obtained, especially the variation relations between the quantum discords and the parameters characterizing the WLQCC states. By virtue of numerical computations, quantum discords in a Werner state before and after LQCC protocols are compared. It is found that quantum discord in any WLQCC state cannot exceed that in the original Werner state.

DOI
10.3390/e22020147

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In this paper, quantum discords in a special kind of states, i.e., Werner states by local quantum operations and classical communication (LQCC) protocols (WLQCC states), are studied. Nineteen parameters to quantify the quantum discords are reduced to four parameters in terms of properties of Werner states and quantum discord. In the case of orthogonal projective measures, analytic expression of quantum discords in WLQCC states is analytically worked out. Some properties of the quantum discord in the WLQCC states are obtained, especially the variation relations between the quantum discords and the parameters characterizing the WLQCC states. By virtue of numerical computations, quantum discords in a Werner state before and after LQCC protocols are compared. It is found that quantum discord in any WLQCC state cannot exceed that in the original Werner state.
Abstract Werner derivatives are a special kind of mixing states that originate from the Werner state due to unitary evolutions. In this paper, quantum correlation (QC) swapping between two Werner derivatives is studied. Quantum discord (Ollivier and Zurek 2001 Phys. Rev. Lett. 88 017901) is employed as the QC quantifier to characterize and quantify all QCs inhabited in the states which emerge during the swapping process. All concerned QCs are analytically or numerically worked out and their behaviors and properties such as monotony features and thresholds are concretely analyzed. Particularly, the QC properties of the four different final states corresponding to four different Bell states are revealed, compared and discussed. More importantly, it is found that, long-distance shared QCs can be generated from two short-distance ones via Bell-state measures in the middle nodes of a quantum network.
The Generalized Werner-Like states (GWLs) are a class of non--X states in which the exchange operator is replaced for a generic one-rank projector in the Werner states. We obtained an exact analytical expression of Quantum Discord for these states. The optimization problem involved is solved by giving an analytical expression, in exact form for the conditional entropy. We compared the Quantum Discord (QD) with the Entanglement of Formation (EoF) for the same states. The pure states of GWLs with equal concurrence have the same QD and EoF.
Abstract Quantum teleportation fundamentally depends on shared quantum correlations between spatially separated parties. Although entanglement is widely recognized as the primary resource enabling teleportation, quantum discord represents a more general form of nonclassical correlations that can persist even when entanglement is absent. We provide a thorough analysis combining analytical and numerical evaluations of quantum discord, negativity, and concurrence across varying noise parameters. The study includes simulations under both ide-alized and realistic noisy conditions, incorporating depolarizing noise models alongside experimentally relevant constraints. To improve quantum fidelity and accurately characterize quantum correlations in noisy environments, advanced error mitigation techniques—such as measurement error correction and zero-noise extrapolation—are applied. In this study, we focus on teleportation protocols utilizing two-qubit Werner states, which constitute a significant class of noisy mixed states modeling imperfect entanglement. We systematically examine how the teleportation fidelity varies as a function of the Werner mixing parameter λ and investigate its relationship with the corresponding quantum discord. Our findings indicate that quantum discord remains strictly greater than zero even in parameter regions where entanglement vanishes, emphasizing the role of discord in sustaining quantum advantages in teleportation schemes exposed to noise and imperfections. This highlights the importance of considering non-entanglement quantum correlations for a comprehensive understanding of teleportation resources in realistic settings.
Abstract Using the single-mode approximation we study the quantum correlations of a free Dirac field on the Werner state in the noninertial frame. We present analytical quantum discord D and its geometric measurement D G . We notice that the quantum discord still exists for the system ρ ARI even in the acceleration limit. We also calculate the entanglement of formation (EOF) and the geometric measure of entanglement ( E G ) to compare the behaviors of the entanglement with the quantum discord. The entanglement is nonzero for the fidelity of the Werner state with a Bell state F > 0.5, while the quantum discord is equal to zero only for F = 0.25. We also observe that the quantum discord is more robust to the change of acceleration than the entanglement, which is more sensitive to the acceleration.
We investigate quantum discord of the "q-deformed" Werner state via Yang–Baxterization approach. There are two parameters q and u in this "q-deformed" Werner state. The parameter u, which plays an important role in some typical models, is related to the probability of the "q-deformed" two-qubit spin singlet state in this study. The "q-deformed" parameter q is related to the single loop through d = q + q-1. When topological parameter d approaches 2 (i.e. q → 1), the "q-deformed" Werner state degenerates into the well-known Werner state. The results show that topological parameter d has great influence on quantum correlations of the "q-deformed" Werner state. When we fix the parameter u, the quantum correlations decrease with increasing the single loop d. When d approaches +∞ (i.e. q → 0+or +∞), quantum discord, geometric measure of quantum discord and entanglement all tend to 0. While d approaches 2 (i.e. q → 1), all of them just have the same results with the Werner state.
Present work is an attempt to compare quantum discord and quantum entanglement of Werner states formed with the four bipartite entangled coherent states (ECS) used recently for quantum teleportation of a qubit encoded in superposed coherent state. Out of these, two based on maximally ECS are exactly similar to the perfect Werner state, while the rest two, based on non-maximally ECS, which are called quasi-Werner states behave in somewhat different ways and their quantum discord and entanglement depends on the coherent amplitude and the measurement basis.