Abstract:

In the context of quantum information theory, the positive mapping St?rmer-Woronowicz feature is only applicable to low dimensions, the positive partial transposition (PPT) of the mixed quantum state does not form a necessary and sufficient condition for separability in a higher dimensional Hilbert space, so PPT entanglement states exists. Bound entanglement is a weak form of quantum entanglement. It cannot purify any entanglement under local operation and classical communication, which means that not all entanglement can be directly applied to quantum communication. How to characterize bound entanglement states is one of the key problems in quantum information. Bound entanglement states can be constructed by means of an unexpandable product basis. In this paper, we give a constructon of unextensible product basis for mixed quantum states in high dimensional systems, and give the rule of the number of basis vectors in this basis.

Key words: Positive map, Positive partial transposition, Separability criterion, Unextensible product basis, Entanglement state