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arXiv:1003.5153 · Physical Review A

Connection among entanglement, mixedness, and nonlocality in a dynamical context

Laura Mazzola, Bruno Bellomo, Rosario Lo Franco, Giuseppe Compagno

Published May 20, 2010• 61 citations
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Abstract

We investigate the dynamical relations among entanglement, mixedness, and nonlocality, quantified by concurrence $C$, purity $P$, and maximum 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 multibranch curve in the $C$-$P$-$B$ space and we show that a closed relation among these quantifiers does not hold. By extending the known relation between $C$ and $B$ for pure states, we give an expression among the three quantifiers for mixed states. In this equation we introduce a quantity, vanishing for pure states, which in general does not have 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.

DOI
10.1103/physreva.81.052116

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We study the exact entanglement and entropy dynamics of two qubits interacting with a common zero-temperature non-Markovian reservoir. It is a commonly held view that entanglement loss due to environmental decoherence is accompanied by loss of purity of the state of the system. We demonstrate that such an intuitive picture does not always apply: the deterioration of entanglement and purity does not necessarily come together; i.e. revivals of entanglement can be accompanied by deterioration of purity. To complete our investigation on entanglement–mixedness interplay we consider the case of initial mixed states and study how the entanglement dynamics and its revivals are related to both the initial purity and the initial entanglement.
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The maximally entangled state can be the mixed state form beside the well-known pure state case. As quantified by the negativity, we study the entanglement dynamics of bipartite mixed maximally entangled state (MMES) in multipartite cavity-reservoir systems. It is found that the MMES can exhibit the phenomenon of entanglement sudden death, which is quite different to the asymptotic decay of pure state case. Moreover, we find that the maximal entanglement cannot guarantee the maximal nonlocality. The measurement-induced nonlocality (MIN) of MMES is not always the maximal, and its value and dynamical behavior are dependent on the mixed probability. In addition, we investigate the distributions of negativity and MIN in the multipartite system, where the two types of correlations have different monogamous properties in the dynamical procedure.
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We study the entanglement dynamics of three two-level atoms interacting with a structured reservoir. The atoms are initially prepared in a mixed W state while the reservoir is in the vacuum. We show the dependence of entanglement dynamics on the purity of initial atomic state and on the amount of non-Markovianity. When the initial state of atoms is in a W pure state, the entanglement will decay asymptotically, while it vanishes in a finite time if the initial state is in a mixed W state. In addition, as the memory effect of the environment, entanglement can partially revive after it vanishes, and the revival degree is dependent on the strength of non-Markovian effect. In the end, we consider the entanglement generation and its evolution when the initial state of the atoms system is completely separable.
The maximally entangled state can be in a mixed state as well as the well-known pure state. Taking the negativity as a measure of entanglement, we study the entanglement dynamics of bipartite, mixed maximally entangled states (MMESs) in multipartite cavity-reservoir systems. It is found that the MMES can exhibit the phenomenon of entanglement sudden death, which is quite different from the asymptotic decay of the pure-Bell-state case. We also find that maximal entanglement cannot guarantee maximal nonlocality, and the MMES does not correspond to the state with maximal measurement-induced nonlocality (MIN). In fact, the value and dynamic behavior of the MIN for the MMESs are dependent on the mixed-state probability. In addition, we investigate the distributions of negativity and the MIN in a multipartite system, where the two types of correlations have different monogamous properties.