Schmidt-number witnesses and bound entanglement - art. no. 050301

The Schmidt number of a mixed state characterizes the minimum Schmidt lank of the pure states needed to construct it. We investigate the Schmidt numbe r of an arbitrary mixed state by studying Schmidt-number witnesses that det ect it. We present a canonical form of such witnesses and provide construct ive methods far their optimization. Finally, we present strong evidence tha t all bound entangled states with positive partial transpose in C(3)circle timesC(3) have Schmidt number 2.