Article ID Journal Published Year Pages File Type
1901026 Reports on Mathematical Physics 2013 16 Pages PDF
Abstract

The realignment operation and the computable cross norm or realignment (CCNR) criterion of separability for states in infinite-dimensional bipartite quantum systems are established. Let HA and HB be complex Hilbert spaces with dim HA ⊕ HB ≤ +∞. Let ρ be a quantum state acting on HA ⊕ HB and {δk} be the Schmidt coefficients of ρ as a vector in the Hilbert space C2(HA) ⊕ C2(HB). We introduce the realignment operator ρR and the computable cross norm ||ρ||CCN of ρ and show that if ρ is separable, then ||ρR||Tr = ||ρ||CCN = Σk δ ≤ 1. In particular, if ρ is a pure state, then ρ is separable if and only if ||ρR||Tr = ||ρ||CCN = Σk δk = 1. For the finite-dimensional case, this recovers the original computable cross norm criterion.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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