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Register a new userRealignment separability criterion assisted with filtration for detecting continuous-variable entanglement
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We introduce a weak form of the realignment separability criterion which is particularly suited to detect continuous-variable entanglement and is physically implementable (it requires linear optics transformations and homodyne detection). Moreover, we define a family of states, called Schmidt-symmetric states, for which the weak realignment criterion reduces to the original formulation of the realignment criterion, making it even more valuable as it is easily computable especially in higher dimensions. Then, we focus in particular on Gaussian states and introduce a filtration procedure based on noiseless amplification or attenuation, which enhances the entanglement detection sensitivity. In some specific examples, it does even better than the original realignment criterion.
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Currently available separability criteria for continuous-variable states are generally based on the covariance matrix of quadrature operators. The well-known separability criterion of Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] , for example, gives a necessary and sufficient condition for a two-mode Gaussian state to be separable, but leaves many entangled non-Gaussian states undetected. Here, we introduce an improvement of this criterion that enables a stronger entanglement detection. The improved condition is based on the knowledge of an additional parameter, namely the degree of Gaussianity, and exploits a connection with Gaussianity-bounded uncertainty relations [Phys. Rev. A 86, 030102 (2012)]. We exhibit families of non-Gaussian entangled states whose entanglement remains undetected by the Duan-Simon criterion.
The present paper is devoted to investigation of the entropy reduction and entanglement-assisted classical capacity (information gain) of continuous variable quantum measurements. These quantities are computed explicitly for multimode Gaussian measurement channels. For this we establish a fundamental property of the entropy reduction of a measurement: under a restriction on the second moments of the input state it is maximized by a Gaussian state (providing an analytical expression for the maximum). In the case of one mode, the gain of entanglement assistance is investigated in detail.
The content of this paper is now available as part of arXiv:0802.2019
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