Wednesday, June 19, 2013

1306.4166 (Wataru Kumagai et al.)

Second Order Asymptotics of Optimal Approximate Conversion for
Probability Distributions and Entangled States and Its Application to LOCC

Wataru Kumagai, Masahito Hayashi
We consider approximate conversion problems for probability distributions and derive the asymptotically optimal second-order conversion rate for independent and identical distributions on finite sets. Then, we apply those results to approximate conversion problems of entangled pure states in quantum systems when only local operations and classical communiactions (LOCC) are allowed. Our results can be regarded as a generalization of those for the resolvability and the intrinsic randomness, and the quantum application of our results can be regarded as a generalization of those for the entanglement dilution and concentration. Moreover, we will introduce the notion of LOCC cloning for a known pure entangled state and derive its optimal asymptotic performance. To derive the optimal second-order rates, the majorization method is used, which is a basic tool in the conversion theory of quantum entangled pure states by LOCC. In this paper, we show the efficiency of the majorization method not only in quantum settings but also in classical settings.
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