Schmidt number witnesses and bound entanglement

Details Schmidt number witnesses and bound entanglement Schmidt number witnesses and bound entanglement

2000-09-26

arxiv.org/abs/quant-ph/0009109v2

Phys. Rev. A 63, 050301 (2001)

Physics

Quantum Physics

5 pages, Latex, no figures.Corrected version. An observation from the previous version has been withdrawn and a new proof adde

Scientific paper

10.1103/PhysRevA.63.050301

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 constructing a Schmidt number witness that detects 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 two qutrit systems have Schmidt number 2.

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