Entanglement, Purity, and Information Entropies in Continuous Variable Systems

Abstract

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.

16 pages, 5 low-res figures, OSID style. Presented at the International Conference ``Entanglement, Information and Noise'', Krzyzowa, Poland, June 14--20, 2004

References in corpus (15)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• Extremal entanglement and mixedness in continuous variable systems
• Maximal entanglement versus entropy for mixed quantum states
• Entanglement of formation for symmetric Gaussian states
• Symplectic invariants, entropic measures and correlations of Gaussian states
• Maximally entangled mixed states in two qubits
• Purity of Gaussian states: measurement schemes and time-evolution in noisy channels
• Determination of continuous variable entanglement by purity measurements
• Quantification and scaling of multipartite entanglement in continuous variable systems
• How to measure squeezing and entanglement of Gaussian states without homodyning
• Pulsed squeezed vacuum characterization without homodyning
• Characterizing entanglement with global and marginal entropic measures

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• On uncertainty relations and entanglement detection with mutually unbiased measurements
• Extra phase noise from thermal fluctuations in nonlinear optical crystals
• Boosting entanglement generation in down-conversion with incoherent illumination
• Distance and Coupling Dependence of Entanglement in the Presence of a Quantum Field
• Gaussian maximally multipartite entangled states
• Certifying the purity of quantum states with temporal correlations
• Unified framework to determine Gaussian states in continuous variable systems
• Mixedness and entanglement for two-mode Gaussian states
• Generation of entanglement and non-stationary states via competing coherent and incoherent bosonic hopping
• Minkowski structure for purity and entanglement of Gaussian bipartite states
• Purity Temperature Dependent for Coupled Harmonic Oscillators
• Effective thermodynamics of isolated entangled squeezed and coherent states