Quantum channels that preserve entanglement

Details Quantum channels that preserve entanglement Quantum channels that preserve entanglement

2008-01-16

arxiv.org/abs/0801.2531v2

Mathematics

Operator Algebras

14 pages, links to references are now fixed

Scientific paper

Let M and N be full matrix algebras. A unital completely positive (UCP) map \phi:M\to N is said to preserve entanglement if its inflation \phi\otimes \id_N : M\otimes N\to N\otimes N has the following property: for every maximally entangled pure state \rho of N\otimes N, \rho\circ(\phi\otimes \id_N) is an entangled state of M\otimes N. We show that there is a dichotomy in that every UCP map that is not entanglement breaking in the sense of Horodecki-Shor-Ruskai must preserve entanglement, and that entanglement preserving maps of every possible rank exist in abundance. We also show that with probability 1, {\em all} UCP maps of relatively small rank preserve entanglement, but that this is not so for UCP maps of maximum rank.

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