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Communications in Theoretical Physics

Entanglement Capacity of Two-Qubit Unitary Operator with the Help of Auxiliary System

Baolin Hu, Yao-Min Di

Published Jun 1, 2007• 6 citations
Publisher

Abstract

The entanglement capacity of general two-qubit unitary operators is studied when auxiliary systems are allowed, and the analytical results based on linear entropy when input states are disentangled are given. From the results the condition for perfect entangler, α 1 = α 2 = π/4, is obtained. Contrary to the case without auxiliary system, the parameter α 3 may play active role to the entanglement capacity when auxiliary systems are allowed.

DOI
10.1088/0253-6102/47/6/012

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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.
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Abstract The entangling power of a bipartite unitary operation shows the maximum created entanglement with the product input states. For an arbitrary two-qubit unitary operation, it is sufficient to consider its normalized operation U with parameters and c 3 . We show how to compute the entangling power of U when . In particular we construct the analytical expressions of entangling power of such U for two examples. We also formulate the entangling power of bipartite unitary operations of Schmidt rank two for any dimensions.