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Quantum Correlation Based on Uhlmann Fidelity for Gaussian States

1,†, 2,*,† and 3,4,†
1
College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China
2
College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
3
Department of Mathematics, Shanxi University, Taiyuan 030006, China
4
Institute of Big Data Science and Industry, Shanxi University, Taiyuan 030006, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2019, 21(1), 6; https://doi.org/10.3390/e21010006
Received: 20 September 2018 / Revised: 14 December 2018 / Accepted: 19 December 2018 / Published: 22 December 2018
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Abstract

A quantum correlation N F G , A for ( n + m ) -mode continuous-variable systems is introduced in terms of local Gaussian unitary operations performed on Subsystem A based on Uhlmann fidelity F. This quantity is a remedy for the local ancilla problem associated with the geometric measurement-induced correlations; is local Gaussian unitary invariant; is non-increasing under any Gaussian quantum channel performed on Subsystem B;and is an entanglement monotone when restricted to pure Gaussian states in the ( 1 + m ) -mode case. A concrete formula for ( 1 + 1 ) -mode symmetric squeezed thermal states (SSTSs) is presented. We also compare N F G , A with other quantum correlations in scale, such as Gaussian quantum discord and Gaussian geometric discord, for two-mode SSTSs, which reveals that N F G , A has some advantage in detecting quantum correlations of Gaussian states. View Full-Text
Keywords: quantum correlations; Gaussian states; Uhlmann fidelity; Gaussian unitary operators quantum correlations; Gaussian states; Uhlmann fidelity; Gaussian unitary operators
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Liu, L.; Hou, J.; Qi, X. Quantum Correlation Based on Uhlmann Fidelity for Gaussian States. Entropy 2019, 21, 6.

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