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Schmidt-number witnesses and bound entanglement

Anna Sanpera, Dagmar Bruß, and Maciej Lewenstein
Phys. Rev. A 63, 050301(R) – Published 9 April 2001
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Abstract

The Schmidt number of a mixed state characterizes the minimum Schmidt rank of the pure states needed to construct it. We investigate the Schmidt number of an arbitrary mixed state by studying Schmidt-number witnesses that detect it. We present a canonical form of such witnesses and provide constructive methods for their optimization. Finally, we present strong evidence that all bound entangled states with positive partial transpose in C3C3 have Schmidt number 2.

  • Received 11 October 2000

DOI:https://doi.org/10.1103/PhysRevA.63.050301

©2001 American Physical Society

Authors & Affiliations

Anna Sanpera, Dagmar Bruß, and Maciej Lewenstein

  • Institut für Theoretische Physik, Universität Hannover, 30169 Hannover, Germany

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Vol. 63, Iss. 5 — May 2001

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