Entanglement Bounds for a Family of Two-Mode Gaussian States

Jiang, Liangxiao

doi:10.1142/s0219749904000201

Cited by 7 publications

(10 citation statements)

References 19 publications

(15 reference statements)

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“…However, the situation is different for other special TMGS's. In the STS case, the Gaussian entanglement measured by Bures distance [9] and the Gaussian EoF [11] are found to be in agreement. They are nicely depending on the same parameter, the difference between the two-mode squeeze parameter r and its value r s defining the separability threshold.…”

Section: Introductionsupporting

confidence: 51%

“…The parameter r − r s cannot be expressed in terms of onlyκ − . Therefore, the negativity of a STS is not equivalent to the two Gaussian measures of its entanglement evaluated at present [9,11]. A similar disagreement between the Gaussian EoF and the negativity of the Gaussian states having extremal negativity at fixed global and local purities [12] was recently noticed in Ref.…”

Section: Introductionmentioning

confidence: 55%

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Gaussian entanglement of symmetric two-mode Gaussian states

Marian

2008

Eur. Phys. J. Spec. Top.

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A Gaussian degree of entanglement for a symmetric two-mode Gaussian state can be defined as its distance to the set of all separable two-mode Gaussian states. The principal property that enables us to evaluate both Bures distance and relative entropy between symmetric two-mode Gaussian states is the diagonalization of their covariance matrices under the same beam-splitter transformation. The multiplicativity property of the Uhlmann fidelity and the additivity of the relative entropy allow one to finally deal with a single-mode optimization problem in both cases. We find that only the Bures-distance Gaussian entanglement is consistent with the exact entanglement of formation.

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Section: Introductionsupporting

confidence: 51%

Section: Introductionmentioning

confidence: 55%

Gaussian entanglement of symmetric two-mode Gaussian states

Marian

2008

Eur. Phys. J. Spec. Top.

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“…Note that the STSs are important non-symmetric TMGSs that can be produced experimentally and are used in the protocols for quantum teleportation. Interestingly, in the STS-case the Gaussian entanglement measured by Bures distance [16] and the Gaussian EF [11] were found to be in agreement. They are monotonous functions of the same parameter [17] which cannot be expressed only in terms of k − .…”

Section: Introductionmentioning

confidence: 59%

“…They are monotonous functions of the same parameter [17] which cannot be expressed only in terms of k − . Therefore, the negativity of a STS is not equivalent to the two Gaussian measures of entanglement evaluated at present [11,16].…”

Section: Introductionmentioning

confidence: 98%

Bures distance as a measure of entanglement for symmetric two-mode Gaussian states

Marian

2008

Phys. Rev. A

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We evaluate a Gaussian entanglement measure for a symmetric two-mode Gaussian state of the quantum electromagnetic field in terms of its Bures distance to the set of all separable Gaussian states. The required minimization procedure was considerably simplified by using the remarkable properties of the Uhlmann fidelity as well as the standard form II of the covariance matrix of a symmetric state. Our result for the Gaussian degree of entanglement measured by the Bures distance depends only on the smallest symplectic eigenvalue of the covariance matrix of the partially transposed density operator. It is thus consistent to the exact expression of the entanglement of formation for symmetric two-mode Gaussian states. This non-trivial agreement is specific to the Bures metric.

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“…The state is a x-p symmetric Gaussian state [9] whose Gaussian relative entropy of entanglement can be obtained [10]. The separability criterion now is α 2…”

Section: The Inter-mode Amplifiermentioning

confidence: 99%