Physics – Quantum Physics
Scientific paper
2005-04-27
Russian Math. Surveys, vol. 60, N2,2005
Physics
Quantum Physics
12 pages
Scientific paper
In this paper we give a general integral representation for separable states in the tensor product of infinite dimensional Hilbert spaces and provide the first example of separable states that are not countably decomposable. We also prove the structure theorem for the quantum communication channels that are entanglement-breaking, generalizing the finite-dimensional result of M. Horodecki, Ruskai and Shor. In the finite dimensional case such channels can be characterized as having the Kraus representation with operators of rank 1. The above example implies existence of infinite-dimensional entanglement-breaking channels having no such representation.
Holevo Alexander S.
Shirokov M. E.
Werner Reinhard F.
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