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

Marian, Paulina; Marian, Tudor A.

doi:10.1103/physreva.77.062319

Cited by 39 publications

(35 citation statements)

References 37 publications

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“…In this vein, it is worth stressing that distance measures have been successfully employed in assessing a number of disputed quantities, such as nonclassicality [21][22][23], entanglement [24][25][26], information [27][28][29], non-Gaussianity [30], and localization [31,32], to cite only a few examples.…”

Section: Introductionmentioning

confidence: 99%

Classical distinguishability as an operational measure of polarization

et al. 2014

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We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all of its polarization-transformed counterparts. By using the Hilbert-Schmidt metric, the resulting degree is a sum of two terms: one is the purity of the state and the other can be interpreted as a classical distinguishability, which can be experimentally determined in an interferometric setup. For transverse fields, this reduces to the standard approach, whereas it allows one to get a straight expression for nonparaxial fields.

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Section: Introductionmentioning

confidence: 99%

Classical distinguishability as an operational measure of polarization

et al. 2014

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“…Notice that definition (5.13) implies the equality B 1 = B 2 =: B. The explicit symplectic eigenvalues of the CM of a symmetric two-mode GS [48], …”

Section: Symmetric Two-mode Gaussian Statesmentioning

confidence: 99%

Hellinger distance as a measure of Gaussian discord

Marian¹,

Marian²

2015

J. Phys. A: Math. Theor.

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Abstract. Especially investigated in recent years, the Gaussian discord can tentatively be quantified by a distance between a given two-mode Gaussian state and the set of all the zero-discord two-mode Gaussian states. However, as this set consists only of product states, such a distance captures all the correlations (quantum and classical) between modes. Therefore it is merely un upper bound for the geometric discord, no matter which is the employed distance. In this work we choose for this purpose the Hellinger metric that is known to have many beneficial properties recommending it as a good measure of quantum behaviour. In general, this metric is determined by affinity, a relative of the Uhlmann fidelity with which it shares many important features. As a first step of our work, the affinity of a pair of n-mode Gaussian states is written. Then, in the two-mode case, we succeeded in determining exactly the closest Gaussian product state and computed the Gaussian discord accordingly. The obtained general formula is remarkably simple and becomes still friendlier in the significant case of symmetric two-mode Gaussian states. We then analyze in detail two special classes of two-mode Gaussian states of theoretical and experimental interest as well: the squeezed thermal states and the mode-mixed thermal ones. The former are separable under a well-known threshold of squeezing, while the latter are always separable. It is worth stressing that for symmetric states belonging to either of these classes, we find consistency between their geometric Hellinger discord and the originally defined discord in the Gaussian approach. At the same time, the Gaussian Hellinger discord of such a state turns out to be a reliable measure of the total amount of its cross correlations.

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“…It is called the Transfer Function of the setup, and has the one-mode phase space coordinate ξ as argument. For a Gaussian two mode resource state, this has been shown to correspond to a one-mode Gaussian characteristic function [14], amounting in the output state to a distorting Gaussian noise.…”

Section: Averages Of Observables For the Teleportation Output 21 Thementioning

confidence: 99%

“…The expectation value for â †â is given in equation (14). Note that the first order averages â AB , â † AB corresponding to the two-mode squeezed resource transfer function (see equation (13)) are equal to zero.…”

Section: Expectation Value Of the Two-photon Correlation Function G 2mentioning

confidence: 99%

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Optimization of the transmission of observable expectation values and observable statistics in continuous-variable teleportation

Farias

Stephany

2010

Phys. Rev. A

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We analyze the statistics of observables in continuous variable (CV) quantum teleportation in the formalism of the characteristic function. We derive expressions for average values of output state observables in particular cumulants which are additive in terms of the input state and the resource of teleportation..Working with a general class of teleportation resources, the Squeezed Bell-like states, which may be optimized in a free parameter for better teleportation performance [1] we discuss the relation between resources optimal for fidelity and for different observable averages. We obtain the values of the free parameter of the Squeezed Bell-like states which optimize the central momenta and cumulants up to fourth order. For the cumulants the distortion between in and out states due to teleportation depends only on the resource. We obtain optimal parameters ∆ opt (2) and ∆ opt (4) for the second and fourth order cumulants which do not depend on the squeezing of the resource. The second order central momenta which is equal to the second order cumulants and the photon number average are also optimized by the resource with ∆ opt (2) . We show that the optimal fidelity resource which has been found in reference [1] to depend also on the characteristics of input tends for high squeezing to the resource which optimizes the second order momenta. A similar behavior is obtained for the resource which optimizes the photon statistics which is treated here using the sum of the squared differences in photon probabilities of input and output states as the distortion measure. This is interpreted naturally to mean that the distortions associated to second order momenta dominates the behavior of the output state for large squeezing of the resource. Optimal fidelity resources and optimal photon statistics resources are compared and is shown that for mixtures of Fock states both resources are equivalent.

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

Cited by 39 publications

References 37 publications

Classical distinguishability as an operational measure of polarization

Classical distinguishability as an operational measure of polarization

Hellinger distance as a measure of Gaussian discord

Optimization of the transmission of observable expectation values and observable statistics in continuous-variable teleportation

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