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Physical Review A

Distillability of two entanglement particles transmitted through a noisy channel

X. X. Yi, Guang‐Can Guo

Published Nov 14, 2000• 1 citation
Publisher

Abstract

A quantum system is called separable if its density matrix can be written as a mixture of product states. In this paper we apply the separability criterion as well as the distillability criterion to show that any initial inseparable $2\ifmmode\times\else\texttimes\fi{}2$ system retains its inseparability after its transmission through a noisy channel which consists of a set of harmonic oscillators. Hence the final state of the system can be distilled to a singlet form. For higher dimensions, however, this result is no longer true in general. The distillability of a state with higher dimensions after its transmission through the noisy channel is also discussed in this paper.

DOI
10.1103/physreva.62.062312

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We apply the inseparability criterion for 2×22 \times 22×2 systems, local filtering and Bennett et al. purification protocol [Phys. Rev. Lett. {\bf 76}, 722 (1996)] to show how to distill {\it any} inseparable 2×22\times 22×2 system. The extended protocol is illustrated geometrically by means of the state parameters in the Hilbert-Schmidt space.