Phys. Rev. Lett. 86, 3658–3661 (2001)Bound Entangled Gaussian StatesReceived 4 October 2000; published in the issue dated 16 April 2001 We discuss the entanglement properties of bipartite states with Gaussian Wigner functions. For the separability, and the positivity of the partial transpose, we establish explicit necessary and sufficient criteria in terms of the covariance matrix of the state. It is shown that, for systems composed of a single oscillator for Alice and an arbitrary number for Bob, positivity of the partial transpose implies separability. However, this implication fails with two oscillators on each side, as we show by constructing a five parameter family of bound entangled Gaussian states. © 2001 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.86.3658
DOI:
10.1103/PhysRevLett.86.3658
PACS:
03.65.Ud, 03.67.-a
|
|
About | Terms and Conditions | Subscriptions | Search | Help
Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement. Physical Review®, Physical Review Letters®, Reviews of Modern Physics®, and Physical Review Special Topics® are trademarks of the American Physical Society.