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Laser Physics Letters

Quantum correlation swapping between Werner and separable states

Chuanmei Xie, Zhanjun Zhang, Jianlan Chen, Xiaofeng Yin

Published Feb 18, 2021• 5 citations
Publisher

Abstract

Abstract In this paper we study quantum correlation (QC) swapping between two different kinds of quantum-correlated states. To be concrete, one is the famous Werner state while another is a kind of separable state. We employ measurement-induced disturbance (Luo 2008 Phys. Rev. A 77 02230) as the quantifier to characterize and quantify QC. We work out QCs in all the concerned states and concretely analyze their behaviors and properties such monotony features and thresholds. We find that a long-distance shared QC can be generated from two short-distance ones via intermediate measure. Moreover, the amount of the long-distance shared QC cannot reach that in the Werner state but that in the separable state.

DOI
10.1088/1612-202x/abe4ca

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Abstract In this paper we study quantum correlation (QC) swapping between two different kinds of quantum-correlated states. To be concrete, one is the famous Werner state while another is a kind of separable state. We employ measurement-induced disturbance (Luo 2008 Phys. Rev. A 77 02230) as the quantifier to characterize and quantify QC. We work out QCs in all the concerned states and concretely analyze their behaviors and properties such monotony features and thresholds. We find that a long-distance shared QC can be generated from two short-distance ones via intermediate measure. Moreover, the amount of the long-distance shared QC cannot reach that in the Werner state but that in the separable state.
In this paper, quantum correlation (QC) swapping between two Werner-like states, which are transformed from Werner states undergoing local and nonlocal unitary operations, are studied. Bell states measures are performed in the middle node to realize the QC swapping and correspondingly final correlated sates are obtained. Two different QC quantifiers, i.e., measurement-induced disturbance (MID) and ameliorated MID, are employed to characterize and quantify all the concerned QCs in the swapping process. All QCs in the concerned states are evaluated analytically and numerically. Correspondingly, their characteristics and properties are exposed in detail. It is exposed that, through the QC swapping process, one can obtain the long-distance QC indeed. Moreover, the similarities of monotony features of MID and AMID between the initial states and final states are exposed and analyzed.
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.
Abstract 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.
Abstract Quantum correlation (QC) swapping is a generalization of quantum entanglement swapping, in which the concerned QCs can be quantum entanglement, QC beyond quantum entanglement, or both of them. In general, QC swapping is different from quantum entanglement swapping. Obviously, the study range of the former is beyond than the latter, and the former can give more interesting and significant applications in quantum information processings. So far, QC swapping has been studied explicitly only for a rather limited set of two-qubit quantum states as the initial states and cases for more general QC swapping with multi-parameter initial states are not known. In this article, we explore the QC swapping case with three-parameter Bell-diagonal (BD) states as the initial states. The familiar QC measure, quantum discord (Ollivier and Zurek 2001 Phys. Rev. Lett. 88 017901), is utilized to quantify all the QCs in the concerned states. It is found that a long-distance shared QC can be acquired through the BD-initial states case of QC swapping. Moreover, some distinct features and characteristics can be exposed.
In contrast to the seminal entanglement-separability paradigm widely used in quantum information theory, we introduce a quantum-classical dichotomy in order to classify and quantify statistical correlations in bipartite states. This is based on the idea that while in the classical description of nature measurements can be carried out without disturbance, in the quantum description, generic measurements often disturb the system and the disturbance can be exploited to quantify the quantumness of correlations therein. It turns out that certain separable states still possess correlations of a quantum nature and indicates that quantum correlations are more general than entanglement. The results are illustrated in the Werner states and the isotropic states, and are applied to quantify the quantum advantage of the model of quantum computation proposed by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)].