科研之友
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摘要
The partial transposition of a two-qubit state has at most one negative eigenvalue and all the eigenvalues lie in [-1/2,1]. In this Brief Report, we extend this result by Sanpera et al. [A. Sanpera, R. Tarrach, and G. Vidal, Phys. Rev. A 58, 826 (1998)] to arbitrary bipartite states. We show that partial transposition of an m circle times n state cannot have more than (m - 1)(n - 1) number of negative eigenvalues. Low-dimensional states have been studied to show the tightness of this result and explicit examples have been provided for mn <= 9. It is also shown that all the eigenvalues of partial transposition lie within [-1/2,1]. Some possible applications are also discussed.
- 出版日期2013-5-2
