Physics – Quantum Physics
Scientific paper
2004-05-19
Phys. Rev. A 70, 030302(R) (2004)
Physics
Quantum Physics
5 pages, no figures, REVTEX 4, Some new results on generalized Bell states added; a few typos corrected in v3
Scientific paper
10.1103/PhysRevA.70.030302
We consider a bipartite mixed state of the form, $\rho =\sum_{\alpha, \beta =1}^{l}a_{\alpha \beta} | \psi_{\alpha}> < \psi_ \beta}| $, where $| \psi_{\alpha}>$ are normalized bipartite state vectors, and matrix $(a_{\alpha \beta})$ is positive semidefinite. We provide a necessary and sufficient condition for the state $\rho $ taking the form of maximally correlated states by a local unitary transformation. More precisely, we give a criterion for simultaneous Schmidt decomposability of $| \psi_{\alpha}>$ for $\alpha =1,2,..., l$. Using this criterion, we can judge completely whether or not the state $\rho $ 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.
Hayashi Masahito
Hiroshima Tohya
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