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 have Schmidt number 2.
- Received 11 October 2000
DOI:https://doi.org/10.1103/PhysRevA.63.050301
©2001 American Physical Society