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Communications in Theoretical Physics

Entanglement Fidelity as a Measure of Preservation of Entanglement in Local Noisy Process

Yang Xiang, Shi‐Jie Xiong

Published Jun 1, 2011• 1 citation
Publisher

Abstract

A new formula of entanglement fidelity has been introduced, which can serve as a measure of the preservation of entanglement between two initially entangled subsystems exposed to local noisy environments. For a simple model we derive analytic expressions of concurrence and entanglement fidelity and draw the relationship between them. We find that such entanglement fidelity exhibits the behavior similar to that of the concurrence in quantum evolutions.

DOI
10.1088/0253-6102/55/6/10

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A new formula of entanglement fidelity has been introduced, which can serve as a measure of the preservation of entanglement between two initially entangled subsystems exposed to local noisy environments. For a simple model we derive analytic expressions of concurrence and entanglement fidelity and draw the relationship between them. We find that such entanglement fidelity exhibits the behavior similar to that of the concurrence in quantum evolutions.
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Entanglement fidelity quantifies how well a quantum channel preserves the correlations between a transmitted system and an inaccessible reference system. We derive closed-form expressions for the entanglement fidelity of several standard quantum noise models, including the random Pauli-XXX, dephasing, depolarizing, Werner-Holevo, generalized Pauli (Weyl), and amplitude-damping channels. For each model, we express the entanglement fidelity in terms of a general input density operatorρ{\rho}ρ, using Schumacher's Kraus-operator approach, which provides a channel-agnostic recipe for any completely positive trace-preserving map with a finite Kraus representation. We then specialize to a communication scenario in which the source emits a two-letter parametric alphabet, thereby making explicit the dependence of entanglement preservation on both channel and source parameters. The resulting expressions enable direct comparisons of channel performance and rankings for representative families of input states.