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Finding a maximally correlated state - Simultaneous Schmidt decomposition of bipartite pure states

2004/05/31 by Tohya Hiroshima, Masahito Hayashi
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physreva.70.030302

published as Phys. Rev. A 70, 030302(R) (2004) · 5 pages, no figures, REVTEX 4, Some new results on generalized Bell states added; a few typos corrected in v3

arxiv created 2004/08/05 · arxiv updated 2009/12/01

Abstract

We consider a bipartite mixed state of the form, ρ=∑α, β=1laαβ | ψα> < ψ_ β| , where | ψα> are normalized bipartite state vectors, and matrix (aαβ) is positive semidefinite. We provide a necessary and sufficient condition for the state ρ taking the form of maximally correlated states by a local unitary transformation. More precisely, we give a criterion for simultaneous Schmidt decomposability of | ψα> for α=1,2,..., l. Using this criterion, we can judge completely whether or not the state ρ is equivalent to the maximally correlated state, in which the distillable entanglement is given by a simple formula. For generalized Bell states, this criterion is written as a simple algebraic relation between indices of the states. We also discuss the local distinguishability of the generalized Bell states that are simultaneously Schmidt decomposable.

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