Entanglement, Purity, and Information Entropies in Continuous Variable Systems

Details Entanglement, Purity, and Information Entropies in Continuous Variable Systems Entanglement, Purity, and Information Entropies in Continuous Variable Systems

2005-06-06

arxiv.org/abs/quant-ph/0506049v1

Open Syst. Inf. Dyn. 12, 189 (2005)

Physics

Quantum Physics

16 pages, 5 low-res figures, OSID style. Presented at the International Conference ``Entanglement, Information and Noise'', Kr

Scientific paper

10.1007/s11080-005-5730-2

Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal ({\em i.e.}referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or in general by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two--mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized $p-$entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary $1 \times N$-mode partitions.

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