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Open Systems & Information Dynamics

Decay of Entanglement Due to Pure Dephasing: the Role of Geometry of Entangled States

Katarzyna Roszak, Paweł Machnikowski, Lucjan Jacak

Published Mar 1, 2007• 1 citation
Publisher

Abstract

The study of the effect that pure dephasing has on the entanglement of a pair of two-level systems shows that complete disentanglement may be caused by partial pure dephasing for some initial entangled states. We examine the behaviour of the entanglement of two confined charge states under the influence of partial pure dephasing introduced by a super-Ohmic reservoir (typical for semiconductors). We classify the set of completely dephasible states and provide an explanation of this effect.

DOI
10.1007/s11080-007-9029-3

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The study of the effect that pure dephasing has on the entanglement of a pair of two-level systems shows that complete disentanglement may be caused by partial pure dephasing for some initial entangled states. We examine the behaviour of the entanglement of two confined charge states under the influence of partial pure dephasing introduced by a super-Ohmic reservoir (typical for semiconductors). We classify the set of completely dephasible states and provide an explanation of this effect.
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We study the robustness and fragility of entanglement of open quantum systems in some exactly solvable models in which the decoherence is caused by a pure dephasing process. In particular, for the toy models presented in this paper, we identify two different time scales, one is responsible for local dephasing, while the other is for entanglement decay. For a class of fragile entangled states defined in this paper, we find that the entanglement of two qubits, as measured by concurrence, decays faster asymptotically than the quantum dephasing of an individual qubit.
Decoherence of qubits is one main limitation in quantum information processing, where the qubits themselves can be mixed because of decoherence and additional decoherence may generated through interactions with a bath. Here, we present a complete study of qubit-environment entanglement in the case of interactions that lead to pure dephasing of the qubit by allowing the initial state of the qubit to be mixed, exceeding previous restrictions. We find that the criteria for separability that hold for pure initial states of the qubit are reduced to witness status. Yet, the evolution of the witnesses reflects the array of features that entanglement can exhibit in the mixed case but are forbidden in the pure-qubit case. Most notably, this includes sudden birth of entanglement as the initial phase of the evolution is typically separable. Moreover, there is a stark numerical advantage to the study of entanglement for large environments when using the witness rather than the traditional measures available. We include the study of entanglement generated between a spin qubit and a sparse spin environment to illustrate the peculiarities of the evolution of entanglement in this case, as well as to emphasize the level of reliability of the entanglement witness.