The generalized partial for infinite-dimensional transposition criterion quantum systems

Siqing Yan, Yu Jing Guo, Jinchuan Hou

Kai Chen, Ling-An Wu

Siqing YanYu GuoJinchuan Hou

The positive partial transposition (PPT) criterion and the realignment criterion constitute two of the most important criteria for detecting entanglement. The general- ized partial transposition (GPT) criterion which contains the PPT criterion and the realignment criterion as special cases, provides a necessary condition for a multipartite state to be separable. Here we extend the GPT criterion to the infinite- dimensional multipartite (bipartite) case and show that it includes multipartite (bipartite) PPT criterion and multipartite (bipartite) realignment criterion as special cases as well.

Chen, K, Wu, L A

We present a generalized partial transposition separability criterion for the density matrix of a multipartite quantum system. This criterion comprises as special cases the famous Peres-Horodecki criterion and the recent realignment criterion in quant-ph/0202121 and quant-ph/0205017. It involves only straightforward matrix manipulations and is easy to apply. A quantitative measure of entanglement based on this criterion is also obtained.

Franco Strocchi

Maciej Lewenstein, J. I. Cirac, Siniša Karnas

We show that all density operators of 2$\times N$--dimensional quantum systems that remain invariant after partial transposition with respect to the first system are separable. Based on this criterion, we derive a sufficient separability condition for general density operators in such quantum systems. We also give a simple proof of the separability criterion in $2\times 2$--dimensional systems [A. Peres, Phys. Rev. Lett {\bf 77}, 1413 (1996)]