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arXiv:1004.3496 · Journal of Physics A Mathematical and Theoretical

The origin of separable states and separability criteria from entanglement-breaking channels

Bang-Hai Wang, Qin Li, Dongyang Long

Published Apr 6, 2011• 1 citation
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Abstract

In this paper, we show that an arbitrary separable state can be the output of a certain entanglement-breaking channel corresponding exactly to the input of a maximally entangled state. A necessary and sufficient separability criterion and some sufficient separability criteria from entanglement-breaking channels are given.
DOI
10.1088/1751-8113/44/18/185305

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We show that the following nontrivial necessary precondition for an entanglement evolution equation for pure Gaussian states under one-sided Gaussian channels holds. Suppose a Gaussian quantum channel acts on one mode of a pure entangled multi-mode Gaussian input state. Then, for a fixed channel, either all output states are entangled or none of them are. In other words, if the input state is Gaussian, pure and entangled, the separability after a one-sided Gaussian quantum channel does not depend on the input state, but only on the channel. Furthermore, a simple linear-algebraic separability criterion allows to decide whether a given channel destroys the entanglement of pure entangled input states or leaves them entangled.
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