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arXiv:1602.07196 · Physical Review A

Entanglement-breaking channels and entanglement sudden death

Laura T. Knoll, Christian Tomás Schmiegelow, O. Jiménez Farías, Stephen Patrick Walborn, M. A. Larotonda

Published Jul 29, 2016• 9 citations

Abstract

The occurrence of entanglement sudden death in the evolution of a bipartite system depends on both the initial state and the channel responsible for the evolution. An extreme case is that of entanglement-breaking channels, which are channels that, acting on only one of the subsystems, drives them to full disentanglement, regardless of the initial state. In general, one can find certain combinations of initial states and channels acting on one or both subsystems that can result in entanglement sudden death or not. Neither the channel nor the initial state are responsible for this effect but their combination. In this paper we show that, for two entangled qubits, when entanglement sudden death occurs, the evolution can be mapped to that of an effective entanglement-breaking channel on a modified initial state. Our results allow to anticipate which states will suffer entanglement sudden death or not for a given evolution. An experiment with polarization-entangled photons demonstrates the utility of this result in a variety of cases.

DOI: 10.1103/physreva.94.012345

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The occurrence of entanglement sudden death in the evolution of a bipartite system depends on both the initial state and the channel responsible for the evolution. An extreme case is that of entanglement-breaking channels, which are channels that, acting on only one of the subsystems, drives them to full disentanglement, regardless of the initial state. In general, one can find certain combinations of initial states and channels acting on one or both subsystems that can result in entanglement sudden death or not. Neither the channel nor the initial state are responsible for this effect but their combination. In this paper we show that, for two entangled qubits, when entanglement sudden death occurs, the evolution can be mapped to that of an effective entanglement-breaking channel on a modified initial state. Our results allow to anticipate which states will suffer entanglement sudden death or not for a given evolution. An experiment with polarization-entangled photons demonstrates the utility of this result in a variety of cases.

Sudden death of entanglement is a well-known effect resulting from the finite volume of separable states. We study the case when the observer has a limited measurement capability and analyze the effective entanglement (i.e., entanglement minimized over the output data). We show that in the well-defined system of two quantum dots monitored by single-electron transistors, one may observe a sudden death of effective entanglement when real, physical entanglement is still alive. For certain measurement setups, this occurs even for initial states for which sudden death of physical entanglement is not possible at all. The principles of the analysis may be applied to other analogous scenarios, such as estimation of the parameters arising from quantum process tomography.

When an initially entangled pair of qubits undergoes local decoherence processes, there are a number of ways in which the original entanglement can spread throughout the multipartite system consisting of the two qubits and their environments. Here, we report theoretical and experimental results regarding the dynamics of the distribution of entanglement in this system. The experiment employs an all optical setup in which the qubits are encoded in the polarization degrees of freedom of two photons, and each local decoherence channel is implemented with an interferometer that couples the polarization to the path of each photon, which acts as an environment. We monitor the dynamics and distribution of entanglement and observe the transition from bipartite to multipartite entanglement and back, and show how these transitions are intimately related to the sudden death and sudden birth of entanglement. The multipartite entanglement is further analyzed in terms of three- and four-partite entanglement contributions, and genuine four-qubit entanglement is observed at some points of the evolution.

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 .