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arXiv:1001.5453 · Journal of Physics A Mathematical and Theoretical

Bound on distributed entanglement

Jeong San Kim, Soojoon Lee

Published Aug 17, 2010• 2 citations
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Abstract

Using the convex-roof extended negativity and the negativity of assistance as quantifications of bipartite entanglement, we consider the possible remotely-distributed entanglement. For two pure states $\ketϕ_{AB}$ and $\ketψ_{CD}$ on bipartite systems $AB$ and $CD$, we first show that the possible amount of entanglement remotely distributed on the system $AC$ by joint measurement on the system $BD$ is not less than the product of two amounts of entanglement for the states $\ketϕ_{AB}$ and $\ketψ_{CD}$ in two-qubit and two-qutrit systems. We also provide some sufficient conditions, for which the result can be generalized into higher-dimensional quantum systems.

DOI
10.1088/1751-8113/43/38/385305

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Using the convex-roof extended negativity and the negativity of assistance as quantifications of bipartite entanglement, we consider the possible remotely-distributed entanglement. For two pure states ∣ϕ⟩AB\ketϕ_{AB}∣ϕ⟩AB​ and ∣ψ⟩CD\ketψ_{CD}∣ψ⟩CD​ on bipartite systems ABABAB and CDCDCD, we first show that the possible amount of entanglement remotely distributed on the system ACACAC by joint measurement on the system BDBDBD is not less than the product of two amounts of entanglement for the states ∣ϕ⟩AB\ketϕ_{AB}∣ϕ⟩AB​ and ∣ψ⟩CD\ketψ_{CD}∣ψ⟩CD​ in two-qubit and two-qutrit systems. We also provide some sufficient conditions, for which the result can be generalized into higher-dimensional quantum systems.
Using the negativity as an entanglement measure, we investigate the possible amount of remotely prepared entanglement. For two identical isotropic states on two-qudit systems 12 and 34, we calculate the average amount of entanglement remotely distributed on the system 13 by joint measurement on the system 24, and show that the remote preparation of entanglement by the generalized Bell measurement is optimal among rank-one measurements if the isotropic states have a certain fidelity with a maximally entangled state in higher dimensional quantum systems, or if the fidelity of the isotropic states is greater than a certain value depending on the dimension. In addition, we construct a measurement better than the generalized Bell measurement with respect to the remote preparation of entanglement when the isotropic states have small fidelity.
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