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arXiv:1202.2993 · Annals of Physics

Bipartite entanglement in systems of identical particles: The partial transposition criterion

Fabio Benatti, Roberto Floreanini B, Ugo Marzolino

Published Feb 20, 2012• 62 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2012.02.002

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Usual separability criteria applicable to distinguishable particles are not applicable to identical particles. Here we show that Partial transposition and symmetrization (or anti symmetrization) of density matrix of bipartite boson systems (fermion systems) can be used to check whether a state is separable or not.By using determinant based separability criteria it has been found that bipartite states of identical particles are always separable. It is found that partial transposition and symmetrization is equivalent to realignment criteria proposed by Wu.
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.