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arXiv:0809.1746 · Journal of Physics A Mathematical and Theoretical

Understanding entanglement sudden death through multipartite entanglement and quantum correlations

Jared H. Cole

Published Mar 10, 2010• 20 citations
arXivHTMLPDF

Abstract

The effect of entanglement sudden death (ESD) can arise when entangling interactions convert purely bipartite entangled states into more generally entangled states. As a result, ESD can also be seen as a function of partitioning of the system, not just of time, as the system partitioning defines different (multipartite) entanglement classes. Computing both geometric entanglement hierarchies and the generalization of concurrence allows one to demonstrate that different methods of analysing quantum correlations provide both qualitative and quantitatively different descriptions of two commonly cited examples of ESD. These results follow directly from the inequivalence of entanglement and quantum correlations, the latter of which can exist in a state without the former.

DOI
10.1088/1751-8113/43/13/135301

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The effect of entanglement sudden death (ESD) can arise when entangling interactions convert purely bipartite entangled states into more generally entangled states. As a result, ESD can also be seen as a function of partitioning of the system, not just of time, as the system partitioning defines different (multipartite) entanglement classes. Computing both geometric entanglement hierarchies and the generalization of concurrence allows one to demonstrate that different methods of analysing quantum correlations provide both qualitative and quantitatively different descriptions of two commonly cited examples of ESD. These results follow directly from the inequivalence of entanglement and quantum correlations, the latter of which can exist in a state without the former.
Entanglement sudden death (ESD), explored through a series of works by Yu and Eberly, supports the notion of entanglement vanishing abruptly and completely at a finite time, even when the underlying open-system dynamics remain smooth. In this article, we revisit the development of ESD from bipartite origins to genuine multipartite entanglement. We first illustrate the canonical mechanism of ESD with two independently damped qubits, for which the concurrence vanishes at a finite time while populations and coherences remain nonzero. We next present our results on multipartite entanglement for generalized GHZ states under depolarization. Global and independent local depolarizing dynamics can be chosen to produce identical reduced evolution for every individual qubit, yet they yield different genuine-multipartite-entanglement sudden death times, whose ordering can reverse with the initial state. For N-qubit GHZ states, this distinction becomes asymptotically stronger since the ESD time scales as 1/N under independent local depolarization, whereas under global depolarization it approaches a finite value in the thermodynamic limit. Echoing a central lesson of Prof. Eberly's work, we report the lifetime of multipartite entanglement is not fixed by the local dynamics, but rather depends on the evolution of the joint quantum state.
We investigate the entanglement dynamics of the bipartite quantum system between two qubits with the dissipative environment. We begin with the standard Markovian master equation in the Lindblad form and the initial state which is prepared in the extended Werner-like state: ρ Φ AB (0). We examine the conditions for entanglement sudden death (ESD) and calculate the corresponding ESD time by the Wootters concurrence. We observe that ESD is determined by the parameters such as the mean occupation number of the environment N , amount of initial entanglement α and the purity r . For N = 0, we get the analytical expressions of both ESD condition and ESD time. For N > 0 we give a theoretical analysis that ESD always occurs, and simulate the concurrence as a function of γ 0 t and one of the parameters N , α and r .
We investigate the entanglement dynamics of two interacting qubits in a common vacuum environment. The inevitable environment interaction leads to entanglement sudden death (ESD) in a two qubit entangled state system. The entanglement dynamics can be modified by the use of local unitary operations (quantum gates), applied on the system during its evolution. We show that these operations not only delays or avoids the ESD but also advances the entanglement revival with high concurrence value depending on the time of operation. We have analytically found out different time windows for switching with different quantum gates so that the ESD can be completely avoided in the subsequent evolution of the system. Our result offers practical applications in the field of quantum information processing where the entanglement is a necessary resource.
Decoherence due to the unwanted interaction between a quantum system and environment leads to the degradation of quantum coherence. In particular, for an entangled state, decoherence makes a loss of entanglement and Bell nonlocality known as entanglement sudden death (ESD), and Bell nonlocality sudden death (BNSD). Here, we theoretically investigate the entanglement and Bell nonlocality of a bipartite entangled state under three types of decoherence, amplitude damping, phase damping, and depolarizing. Our result provides the bound of decoherence strength that does not lose the entanglement and Bell nonlocality. In addition, we find two interesting features. One is that the entanglement can survive even though one of the entangled qubits is affected by a large strength of decoherence if the other qubit is affected by a small enough strength of decoherence except for the depolarizing. The second one is that when a specific form of entangled state is under amplitude damping, the Bell nonlocality shows an asymmetric behavior respect to the decoherence strengths on each qubit. Our work provides comprehensive information on ESD and BNSD for the bipartite entangled state which will be useful to implement quantum information processing in the presence of decoherence.