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Comparing the globalness of bipartite unitary operations: delocalisation power, entanglement cost and entangling power†

Published online by Cambridge University Press:  28 February 2013

AKIHITO SOEDA  and
MIO MURAO
AKIHITO SOEDA
Affiliation:
Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan Email: soeda@eve.phys.s.u-tokyo.ac.jp
MIO MURAO
Affiliation:
Institute for Nano Quantum Information Electronics, The University of Tokyo, Tokyo 113-0033, Japan Email: murao@phys.s.u-tokyo.ac.jp
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Abstract

We compare three different characterisations of the globalness of bipartite unitary operations, namely, delocalisation power, entanglement cost and entangling power, to investigate the global properties of unitary operations. We show that the globalness of the same unitary operation depends on whether input states are given by unknown states representing pieces of quantum information or a set of known states for the characterisation. We extend our analysis of delocalisation power in two ways. First we show that the delocalisation power differs according to whether the global operation is applied to one piece or two pieces of quantum information. Then we introduce a new task called LOCC one-piece relocation, and prove that the controlled-unitary operations do not have enough delocalisation power to relocate one of two pieces of quantum information by adding LOCC.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Special Issue 2: Developments In Computational Models 2010 , April 2013 , pp. 454 - 470
Copyright
Copyright © Cambridge University Press 2013

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Footnotes

†

This work was supported by the Special Coordination Funds for Promoting Science and Technology, Institute for Nano Quantum Information Electronics.

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