PPT from spectra

2005/02/25 by Roland Hildebrand · 1 citation
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physreva.76.052325

6 pages, no figures

arxiv created 2005/02/25 · arxiv updated 2013/05/29

Abstract

In this contribution we solve the following problem. Let H_nm be a Hilbert space of dimension nm, and let A be a positive semidefinite self-adjoint linear operator on H_nm. Under which conditions on the spectrum has A a positive partial transpose (is PPT) with respect to any partition H_n ⊗ H_m of the space H_nm as a tensor product of an n-dimensional and an m-dimensional Hilbert space? We show that the necessary and sufficient conditions can be expressed as a set of linear matrix inequalities on the eigenvalues of A.

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