Abstract
The PPT (positivity under partial transpose) criterion is studied in the context of separability of continuous variable bipartite states. The partial transpose operation admits, in the Wigner representation of quantum mechanics, a geometric interpretation as momentum reversl or mirror reflection in phase space. This recognition leads to uncertainty principles, stronger than the traditional ones, to be obeyed by all PPT (separable as well as bound entangled) states. In the special case of bipartite two-mode systems, the PPT crrterion turns out to be necessary and sufficient condition for separability, for all Gaussian states: a 1 + 1 syatem has no bound entangled Gaussian state. The symplectic group of linear canonical transformations and the representation of these transformations through (metaplectic) unitary Hilbert space operators play an important role in our ananysis.
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Simon, R. (2003). Separability Criterion for Gaussian States. In: Braunstein, S.L., Pati, A.K. (eds) Quantum Information with Continuous Variables. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1258-9_14
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DOI: https://doi.org/10.1007/978-94-015-1258-9_14
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