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Communications in Theoretical Physics

Creation of Entanglement with Nonlocal Operations

Yong Zhang, Cao Wan-Cang, Gui‐Lu Long

Published Oct 1, 2005• 7 citations
Publisher

Abstract

We discuss how to create more entanglement with nonlocal operations acting on two-particle states. For a given nonlocal operation, we find that some input states cannot produce entanglement and some produce the maximal entanglement, and find that any initial entangled states can produce more entanglement than initial product states.
DOI
10.1088/6102/44/4/625

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Abstract We study the optimal way of creating bi-partite entanglement using a general two-qubit in­ teraction. On the one hand, we analyze the entanglement capability of an arbitrary non-local Hamiltonian acting on two qubits. We explicitly calculate the state which maximizes the entangle­ ment produced per time step 81 during the non-local evolution. On the other hand, we determine the maximal amount of entanglement which can be produced by an arbitrary two-qubit gate. We also give the separable state which leads to the output state containing this amount of entanglement. Furthermore, we consider the situation where auxiliary systems are present. Finally, we determine the non-unitary processes which are able to create entanglement from an initially separable state of two systems.
We consider how much entanglement can be produced by a nonlocal two-qubit unitary operation, UAB{U}_{\mathrm{AB}}UAB​---the entangling capacity of UAB.{U}_{\mathrm{AB}}.UAB​. For a single application of UAB,{U}_{\mathrm{AB}},UAB​, with no ancillas, we find the entangling capacity and show that it generally helps to act with UAB{U}_{\mathrm{AB}}UAB​ on an entangled state. Allowing ancillas, we present numerical results from which we can conclude, quite generally, that allowing initial entanglement typically increases the optimal capacity in this case as well. Next, we show that allowing collective processing does not increase the entangling capacity if initial entanglement is allowed.