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Entropy 2018, 20(4), 266; https://doi.org/10.3390/e20040266

Nonclassicality by Local Gaussian Unitary Operations for Gaussian States

1,†
,
1,2,*,†
and
1,3,†
1
Department of Mathematics, Shanxi University, Taiyuan 030006, China
2
Institute of Big Data Science and Industry, Shanxi University, Taiyuan 030006, China
3
Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 19 January 2018 / Revised: 16 March 2018 / Accepted: 6 April 2018 / Published: 11 April 2018
(This article belongs to the Special Issue Quantum Information and Foundations)
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Abstract

A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 N ( ρ A B ) < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 ) -mode Gaussian states and an estimate of N for ( n + m ) -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord. View Full-Text
Keywords: quantum correlations; Gaussian states; Gaussian unitary operations; continuous-variable systems quantum correlations; Gaussian states; Gaussian unitary operations; continuous-variable systems
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Wang, Y.; Qi, X.; Hou, J. Nonclassicality by Local Gaussian Unitary Operations for Gaussian States. Entropy 2018, 20, 266.

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