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arXiv:quant-ph/0307058 · Physical Review A

Numerical analysis of capacities for two-qubit unitary operations

Dominic William Berry, Barry C. Sanders

Published Feb 10, 2005• 4 citations
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Abstract

We present numerical results on the capacities of two-qubit unitary operations for performing communication and creating entanglement. The capacities for communication considered are based upon the increase in Holevo information of an ensemble. Our results indicate that the capacity may be accurately estimated using ensemble sizes and ancilla dimensions of 4. In addition, the calculated values of these capacities were close to, and in some cases equal to, the similarly defined entangling capacities; this result indicates connections between these capacities.

DOI
10.1103/physreva.71.022304

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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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We consider communication between two parties using a bipartite quantum operation, which constitutes the most general quantum mechanical model of two-party communication. We primarily focus on the simultaneous forward and backward communication of classical messages. For the case in which the two parties share unlimited prior entanglement, we give inner and outer bounds on the achievable rate region that generalize classical results due to Shannon. In particular, using a protocol of Bennett, Harrow, Leung, and Smolin, we give a one-shot expression in terms of the Holevo information for the entanglement-assisted one-way capacity of a two-way quantum channel. As applications, we rederive two known additivity results for one-way channel capacities: the entanglement-assisted capacity of a general one-way channel, and the unassisted capacity of an entanglement-breaking one-way channel. 1.