Peres-horodecki separability criterion for continuous variable systems
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Cites background or methods from "Peres-horodecki separability criter..."
...This observation and its application to the inseparability problem of continuous-variable states was a result of Simon 2000 ....
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...8 Simon, 2000; Werner and Wolf, 2001 , ̂k, ̂l = i 2 kl, k,l = 1,2,3, . . . ,2N , 39 with the 2N 2N matrix having the 2 2 matrix J as diagonal entry for each quadrature pair, for example, for N=2, = J 0 0 J , J = 0 1 − 1 0 ....
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...40 A direct consequence of this commutation relation and the non-negativity of the density operator ̂ is the following N-mode uncertainty relation Simon, 2000; Werner and Wolf, 2001 : V N − i 4 0....
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...Simon’s continuous-variable version of the Peres-Horodecki partial-transpose criterion reads as follows Simon, 2000 : det Adet B + 1 16 − det C 2 − Tr AJCJBJCTJ 1 16 det A + det B , 103 where J is the 2 2 matrix from Eq....
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...103 turns out to be both a necessary and a sufficient condition for separability Simon, 2000 ....
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2,781 citations
Cites background from "Peres-horodecki separability criter..."
...For bosonic systems the quadratures x̂ of the bipartite system Aþ B undergo the transformation x̂ ! ðIA TBÞx̂, where IA is the N-mode identity matrix while TB :¼ Mk¼1Z (Simon, 2000)....
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...…the uncertainty principle is equivalent to the bona fide conditions (Serafini, 2006; Pirandola, Serafini, and Lloyd, 2009) V > 0; detV 1; and 1þ detV: (55) An important class of two-mode Gaussian states has a covariance matrix in the standard form (Duan et al., 2000; Simon, 2000) V ¼ aI C C bI !...
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