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arXiv:0906.0430 · Physical Review A

Entanglement monogamy and entanglement evolution in multipartite systems

Yan-Kui Bai, Ming-Yong Ye, Z. D. Wang

Published Oct 15, 2009• 86 citations
arXivHTMLPDF

Abstract

We analyze the entanglement distribution and the two-qubit residual entanglement in multipartite systems. For a composite system consisting of two cavities interacting with independent reservoirs, it is revealed that the entanglement evolution is restricted by an entanglement monogamy relation derived here. Moreover, it is found that the initial cavity-cavity entanglement evolves completely to the genuine four-partite cavities-reservoirs entanglement in the time interval between the sudden death of cavity-cavity entanglement and the birth of reservoir-reservoir entanglement. In addition, we also address the relationship between the genuine block-block entanglement form and qubit-block form in the interval.

DOI
10.1103/physreva.80.044301

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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.
Abstract This paper contains two main contents. In the first part, we provide two counterexamples of monogamy inequalities for the squared entanglement negativity: one three-qutrit pure state which violates of the He—Vidal monogamy conjecture, and one four-qubit pure state which disproves the squared-negativity-based Regula—Martino—Lee—Adesso-class strong monogamy conjecture. In the second part, we investigate the sharing of the entanglement negativity in a composite cavity-reservoir system using the corresponding multipartite entanglement scores, and then we find that there is no simple dominating relation between multipartite entanglement scores and the entanglement negativity in composite cavity-reservoir systems. As a by-product, we further validate that the entanglement of two cavity photons is a decreasing function of the evolution time, and the entanglement will suddenly disappear interacting with independent reservoirs.
We investigate entanglement dynamics of bipartite as well multipartite systems beyond Markov approximation. We study two pairs of cavity–reservoir systems, modeled as four qubits and track the change of entanglement among cavity–cavity qubits, reservoir–reservoir qubits, and also for genuine entanglement of all four qubits. For cavity–cavity qubits, we find that non-Markovianity prolongs the life of entanglement besides collapse/revival phenomenon. For reservoir–reservoir qubits, entanglement sudden birth is delayed accordingly along with oscillations. For all four qubits, with a specific initial state, we find that genuine entanglement develops gradually, reaches to a maximum constant value and then freezes at this value for some time before decaying. This sudden change in dynamics of genuine entanglement occurs for a time window where neither cavities nor reservoirs are entangled. In contrast to Markov process, sudden change phenomenon may be recurrent in non-Markovian regime.
We study the dynamics of genuine multipartite entanglement for a system of four qubits. Using a computable entanglement monotone for multipartite systems, we investigate the as yet unexplored aspects of a cavity-reservoir system of qubits. For one specific initial state, we observe a sudden transition in the dynamics of genuine entanglement for the four qubits. This sudden change occurs only during a time window where neither cavity-cavity qubits nor reservoir-reservoir qubits are entangled. We show that the sudden change in dynamics of this specific state is extremely sensitive to white noise.
Abstract The distribution of entanglement in a multiparty system can be described by the principle of monogamy. Monogamy is a fundamental characteristic of entanglement that restricts its distribution among more than two parties. In this work, our aim is to explore how quantum entanglement is distributed in accordance with monogamy relations, which utilize both genuine multipartite entanglement measures and bipartite entanglement measures. Specifically, we treat the source entanglement or the accessible entanglement as genuine multipartite entanglement measures and use the entanglement of formation for bipartite cases. For GHZ class states, we analytically demonstrate that the square of the source entanglement serves as an upper bound for the sum of the squares of the entanglement of formation of the reduced subsystems, with some exceptions in specific non-generic GHZ states. We will also present numerical evidence supporting this result for W-class states. In addition, we also explore the monogamy relationship by using accessible entanglement as an upper bound. Our analysis reveals an opposite but consistent pattern in the behavior of monogamy depending on whether source entanglement or accessible entanglement is used as the upper bound. This pattern emphasizes the dual nature of these two measures.