Positive partial transpose from spectra

Roland Hildebrand
Phys. Rev. A 76, 052325 – Published 28 November 2007

Abstract

In this paper we solve the following problem. Let Hnm be a Hilbert space of dimension nm, and let A be a positive semidefinite self-adjoint linear operator on Hnm. Under which conditions on the spectrum has A a positive partial transpose (is PPT) with respect to any partition HnHm of the space Hnm 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 (LMIs) on the eigenvalues of A.

  • Received 10 July 2007

DOI:https://doi.org/10.1103/PhysRevA.76.052325

©2007 American Physical Society

Authors & Affiliations

Roland Hildebrand*

  • LJK, Université Joseph Fourier Grenoble I/CNRS, 51 rue des Mathématiques, BP 53, 38041 Grenoble Cedex 9, France

  • *roland.hildebrand@imag.fr

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Issue

Vol. 76, Iss. 5 — November 2007

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