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.
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.
We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement, the ESD time of mixed states is later than that of the pure state. Finally, we discuss the entanglement distribution in the multipartite system, and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.
We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement, the ESD time of mixed states is later than that of the pure state. Finally, we discuss the entanglement distribution in the multipartite system, and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.
While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximally entangled states and this phenomenon is also observed for other operational measures of nonlocality. In this work, we study a recently proposed measure of nonlocality defined as the probability that a pure state displays nonlocal correlations when subjected to random measurements. We first prove that this measure satisfies some natural properties for an operational measure of nonlocality. Then, we show that for pure states of two qubits the measure is monotonic with entanglement for all correlation two-outcome Bell inequalities: for all these inequalities, the more the state is entangled, the larger the probability to violate them when random measurements are performed. Finally, we extend our results to the multipartite setting.
In this article, we investigate the dynamics of a bipartite system under the action of a local non-Hermitian system. We study the quantum correlation of the bipartite system quantified by the entanglement, measurement-induced nonlocality (MIN) based on Hilbert-Schmidt norm, trace distance, and Bell inequality. We find that the quantum correlations of the system depend on the initial conditions and system parameters. We observe that the states with nonzero quantum correlation obey the Bell inequality even in the absence of entanglement. Moreover, the Bell inequality completely fails to manifest the nonlocality for the mixed quantum state. However, we have identified the nonlocal attributes of the mixed quantum state in terms of MIN and trace distance MIN. Our results show that the trace distance-based correlation is more robust against the nonunitary evolution compared to the other quantifiers.
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.