Nonclassicality by Local Gaussian Unitary Operations for Gaussian States.

Yangyang Wang,Xiaofei Qi,Jinchuan Hou

doi:10.3390/e20040266

Abstract

A measure of nonclassicality in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. 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 , we always have , where the upper bound 1 is sharp. An explicit formula of for -mode Gaussian states and an estimate of for -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation is also compared with entanglement, Gaussian discord and Gaussian geometric discord.

Highlights

The presence of correlations in bipartite quantum systems is one of the main features of quantum mechanics
Recently much attention has been devoted to the study and the characterization of quantum correlations that go beyond the paradigm of entanglement, being necessary but not sufficient for its presence
Different from the finite dimensional case, besides the local Gaussian unitary invariance property for quantum states, we show that N (ρ AB ) = 0 if and only if ρ AB is a Gaussian product state

Summary

Introduction

The presence of correlations in bipartite quantum systems is one of the main features of quantum mechanics. It is important to develop new simple criteria for witnessing correlations beyond entanglement for continuous-variable systems In this direction, Giorda, Paris [12] and Adesso, Datta [13] independently introduced the definition of Gaussian QD for Gaussian states and discussed its properties. We introduce a quantity N in terms of local Gaussian unitary operations for (n + m)-mode quantum states in Gaussian systems. Different from the finite dimensional case, besides the local Gaussian unitary invariance property for quantum states, we show that N (ρ AB ) = 0 if and only if ρ AB is a Gaussian product state This reveals that the quantity N is a kind of faithful measure of the nonclassicality for Gaussian states that a state has this nonclassicality if and only if it is not a product state. We compare N with Gaussian QD and Gaussian GD to illustrate that it is a better measure of the nonclassicality

Gaussian States and Gaussian Unitary Operations

Quantum Correlation Introduced by Gaussian Unitary Operations

Comparison with Other Quantum Correlations

Conclusions