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Chinese Physics Letters

Robustness of Genuine Tripartite Entanglement under Collective Dephasing

Ali Mazhar

Published Jun 1, 2015• 10 citations
Publisher

Abstract

We study the robustness of genuine multipartite entanglement for a system of three qubits under collective dephasing. Using a computable entanglement monotone for multipartite systems, we find that almost every state is quite robust under this type of decoherence. We analyze random states and weighted graph states at infinity and find all of them to be genuinely entangled.

DOI
10.1088/0256-307x/32/6/060302

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We study the robustness of genuine multipartite entanglement for a system of three qubits under collective dephasing. Using a computable entanglement monotone for multipartite systems, we find that almost every state is quite robust under this type of decoherence. We analyze random states and weighted graph states at infinity and find all of them to be genuinely entangled.
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We investigate the distribution of entanglement in tripartite quantum systems under the influence of noisy environment. Entanglement distribution is an important concept to understand the robustness of entanglement in multipartite systems, while preserving multipartite entanglement amid decoherence remains a major challenge. Measuring multipartite entanglement in mixed states under decoherence is challenging. We quantify tripartite entanglement using relative entropy due to its applicability to both pure and mixed states. In this work, we explore how entanglement is distributed among the qubits of multipartite states when the three qubits are exposed to multipartite dephasing setting. In our study we use various pure and mixed tripartite states subjected to both Markovian and non-Markovian Local/Common bosonic reservoir at finite temperature. We show that the robustness of tripartite systems to decoherence depends on the distribution of entanglement and its interaction with various configurations and parameters of the bath.
Multipartite entanglement is an indispensable resource in quantum communication and computation; however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system [Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show that the concurrence fill can be increased under local operations and classical communication (LOCC) on average, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC monotonicity of the three-tangle and find that the bipartite concurrence and the squared concurrence can have distinct performances under the same LOCC. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalized to the multipartite system. Our results shed light on the study of genuine entanglement and also reveal the complex structure of multipartite systems.