Quantum correlations for bipartite continuous-variable systems

2018

Entropy

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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.

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“…If we append an uncorrelated ancilla System C, the state

can be regarded as a bipartite state with the partition A:BC. After some direct calculations, one has:

It is obvious that, as long as

is mixed, the quantity

differs arbitrarily due to local ancilla System C. There are other quantum correlations with a similar ancilla problem, such as the quantum correlations proposed in [ 11 , 16 ]. However, our quantity

keeps unchanged when appending an ancilla system; that is, we have the following result.…”

Section: A Uhlmann Fidelity-based Quantum Correlation and Its Propmentioning

confidence: 99%

“…As is seen,

describes the same correlation in Gaussian states as Gaussian quantum discord (GQD) D , Gaussian geometric discord (GGD)

, the quantum correlation Q proposed in [ 16 ], and

proposed in [ 46 ]. In this section, we will compare

with these QCs for two-mode SSTSs in scale.…”

Section: Comparing With Other Quantum Correlationsmentioning

confidence: 99%

“…For

-mode continuous-variable systems, in [ 16 ],

is a quantum correlation defined in terms of average distance between the reduced states under the LGPOVMs.

where the supremum is taken over all GPOVMs

on the subsystem

, and

.…”

Section: Comparing With Other Quantum Correlationsmentioning

confidence: 99%

“…Gaussian discord of response (

) for two-mode Gaussian states can be found in [ 14 ]. For other related results, see [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum Correlation Based on Uhlmann Fidelity for Gaussian States

2018

Entropy

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“…The MIN for Gaussian states was discussed in [ 11 ]. For other related results, see in [ 12 , 13 , 14 , 15 , 16 , 17 , 18 ], and the references therein. Based on fidelity, in [ 19 ], the authors introduced a quantum correlation

for Gaussian systems.…”

Section: Introductionmentioning

confidence: 99%

A Computable Gaussian Quantum Correlation for Continuous-Variable Systems

2021

Entropy

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Generally speaking, it is difficult to compute the values of the Gaussian quantum discord and Gaussian geometric discord for Gaussian states, which limits their application. In the present paper, for any (n+m)-mode continuous-variable system, a computable Gaussian quantum correlation M is proposed. For any state ρAB of the system, M(ρAB) depends only on the covariant matrix of ρAB without any measurements performed on a subsystem or any optimization procedures, and thus is easily computed. Furthermore, M has the following attractive properties: (1) M is independent of the mean of states, is symmetric about the subsystems and has no ancilla problem; (2) M is locally Gaussian unitary invariant; (3) for a Gaussian state ρAB, M(ρAB)=0 if and only if ρAB is a product state; and (4) 0≤M((ΦA⊗ΦB)ρAB)≤M(ρAB) holds for any Gaussian state ρAB and any Gaussian channels ΦA and ΦB performed on the subsystem A and B, respectively. Therefore, M is a nice Gaussian correlation which describes the same Gaussian correlation as Gaussian quantum discord and Gaussian geometric discord when restricted on Gaussian states. As an application of M, a noninvasive quantum method for detecting intracellular temperature is proposed.

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Computable multipartite multimode Gaussian quantum correlation measure and the monogamy relations for continuous-variable systems

2022

Phys. Rev. A