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Negative Entanglement Measure, and What It Implies

Yu, T, Joseph H. Eberly

Published Mar 10, 2007• 21 citations
OpenAlex

Abstract

In this paper, we extract from concurrence its variable part, denoted $\\Lambda$, and use $\\Lambda$ as a time-dependent measure of "distance", either postive or negative, from the separability boundary. We use it to investigate entanglement dynamics of two isolated but initially entangled qubits, each coupled to its own environment.

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In this paper, we extract from concurrence its variable part, denoted Lambda\\LambdaLambda, and use Lambda\\LambdaLambda as a time-dependent measure of "distance", either postive or negative, from the separability boundary. We use it to investigate entanglement dynamics of two isolated but initially entangled qubits, each coupled to its own environment.
I explore the entanglement dynamics of a three-qubit system in an initial XXX state undergoing decoherence including the possible exhibition of entanglement sudden death. To quantify entanglement I utilize negativity measures and make use of appropriate entanglement witnesses. The negativity results are then extended to XXX states with an arbitraty number of qubits. I also demonstrate nonstandard behavior of the tripartite negativity entanglement metric: its sudden appearance after some amount of decoherence, followed quickly by its disappearance. Finally, I solve for a lower bound on the three-qubit XXX-state concurrence, demonstrate when this bound goes to 000, and outline simplifcations for the calculation of higher-order XXX-state concurrences.
We study the dynamical process of disentanglement of two qubits and two qutrits coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. We use the concurrence and negativity to quantify entanglement of two qubits and two qutrits, respectively. Explicit connections between the concurrence (negativity) and the decoherence factors are given for two initial states, the pure maximally entangled state and the mixed Werner state. We find that the concurrence and negativity decay exponentially with fourth power of time in the vicinity of the critical point of the environmental system.