Separability criteria for continuous variable systems

Abstract

A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the non-negativity of the partially transposed density matrix. This separability criterion is generally more stringent than that used by Simon which is based on the non-negativity of partially transposed density matrix, and thus this criterion may be useful in the analysis of general continuous two-party systems. Another separability criterion used by Duan et al. is shown to be generally weaker than that of Simon. We thus have a hierarchy of separability criteria, but all these criteria when combined with suitable squeezing become equivalent at the boundary of the P-representation condition and thus turned out to be sufficient to analyze the separability of two-party Gaussian systems.

8 pages. To appear in Phys. Rev. A

References in corpus (2)

• Comment on ``Inseparability Criteria for Continuous Bipartite Quantum States''
• The Quantum Separability Problem for Gaussian States

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• Zero-Correlation Entanglement
• Hardy's Paradox and Measurement-disturbance Relations
• Explicit formula of the separability criterion for continuous variables systems