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PPT from spectra

Roland Hildebrand
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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 \otimes 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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Roland Hildebrand. 2005-02-25. PPT from spectra. https://doi.org/10.1103/physreva.76.052325

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