Entropic characterization of Separability in Gaussian states

Abstract

We explore separability of bipartite divisions of mixed Gaussian states based on the positivity of the Abe-Rajagopal (AR) q-conditional entropy. The AR q-conditional entropic characterization provide more stringent restrictions on separability (in the limit q tending to infinity) than that obtained from the corresponding von Neumann conditional entropy (q = 1 case)--similar to the situation in finite dimensional states. Effectiveness of this approach, in relation to the results obtained by partial transpose criterion, is explicitly analyzed in three illustrative examples of two-mode Gaussian states of physical significance.

4 pages, 3 figures; Brief version of the earlier paper; Journal references added

References in corpus (6)

• Quantum information with Gaussian states
• Computable bounds for the discrimination of Gaussian states
• Entanglement of formation for an arbitrary two-mode Gaussian state
• Spectral conditions for entanglement witnesses vs. bound entanglement
• The Quantum Separability Problem for Gaussian States
• Minimal set of local measurements and classical communication for two-mode Gaussian state entanglement quantification

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• Bipartite separability of one parameter families of states using conditional quantum relative Tsallis entropy
• Biseparability of noisy pseudopure, W and GHZ states using conditional quantum relative Tsallis entropy