Connection among entanglement, mixedness and nonlocality in a dynamical context

Abstract

We investigate the dynamical relations among entanglement, mixedness and nonlocality, quantifed by concurrence C, purity P and maximum of Bell function B, respectively, in a system of two qubits in a common structured reservoir. To this aim we introduce the C-P-B parameter space and analyze the time evolution of the point representative of the system state in such a space. The dynamical interplay among entanglement, mixedness and nonlocality strongly depends on the initial state of the system. For a two-excitation Bell state the representative point draws a multi-branch curve in the C-P-B space and we show that a closed relation among these quantifers does not hold. By extending the known relation between C and B for pure states, we give an expression among the three quantifers for mixed states. In this equation we introduce a quantity, vanishing for pure states which has not in general a closed form in terms of C, P and B. Finally we demonstrate that for an initial one-excitation Bell state a closed C-P-B relation instead exists and the system evolves remaining always a maximally entangled mixed state.

8 pages, 3 figures

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• Purity as a witness for initial system-environment correlations in open-system dynamics
• Relations between entanglement and purity in non-Markovian dynamics
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• Statistical distribution of the local purity in a large quantum system
• Quantum Correlations Between Identical and Unidentical Atoms in a Dissipative Environment
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• Nonlinear cross-Kerr quasiclassical dynamics
• Tri-partite non-maximally entangled mixed states as a resource for optimum controlled quantum teleportation fidelity
• Multiphoton resonances for all-optical quantum logic with multiple cavities
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• Entanglement Dynamics for Two Spins in an Optical Cavity---Field Interaction Induced Decoherence and Coherence Revival
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• Non-Markovianity and Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality violation in quantum dissipative systems
• Entanglement versus Bell nonlocality of quantum nonequilibrium steady states
• Tripartite entanglement dynamics in a system of strongly driven qubits
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• Entanglement duality in spin-spin interactions
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• Nonlocality threshold for entanglement under general dephasing evolutions: A case study
• Quantum state transfer and maximal entanglement between distant qubits using a minimal quasicrystal pump