Determination of locally perfect discrimination for two-qubit unitary operations

Determination of locally perfect discrimination for two-qubit unitary operations In the study of local discrimination for multipartite unitary operations, Duan et al. (Phys Rev Lett 100(2):020503, 2008) exhibited an ingenious expression: Any two different unitary operations $$U_1$$ U 1 and $$U_2$$ U 2 are perfectly distinguishable by local operations and classical communication in the single-run scenario if and only if 0 is in the local numerical range of $$U_1^\dag U_2$$ U 1 † U 2 . However, how to determine when 0 is in the local numerical range remains unclear. So it is generally hard to decide the local discrimination of nonlocal unitary operations with a single run. In this paper, for two-qubit diagonal unitary matrices V and their local unitary equivalent matrices, we present a necessary and sufficient condition for determining whether the local numerical range is a convex set or not. The result can be used to easily judge the locally perfect distinguishability of any two unitary operations $$U_1$$ U 1 and $$U_2$$ U 2 satisfying $$U_1^\dag U_2=V$$ U 1 † U 2 = V . Moreover, we design the corresponding protocol of local discrimination. Meanwhile, an interesting phenomenon is discovered: Under certain conditions with a single run, $$U_1$$ U 1 and $$U_2$$ U 2 such that $$U_1^\dag U_2=V$$ U 1 † U 2 = V are locally distinguishable with certainty if and only if they are perfectly distinguishable by global operations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Determination of locally perfect discrimination for two-qubit unitary operations

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-1175-x
Publisher site
See Article on Publisher Site

Abstract

In the study of local discrimination for multipartite unitary operations, Duan et al. (Phys Rev Lett 100(2):020503, 2008) exhibited an ingenious expression: Any two different unitary operations $$U_1$$ U 1 and $$U_2$$ U 2 are perfectly distinguishable by local operations and classical communication in the single-run scenario if and only if 0 is in the local numerical range of $$U_1^\dag U_2$$ U 1 † U 2 . However, how to determine when 0 is in the local numerical range remains unclear. So it is generally hard to decide the local discrimination of nonlocal unitary operations with a single run. In this paper, for two-qubit diagonal unitary matrices V and their local unitary equivalent matrices, we present a necessary and sufficient condition for determining whether the local numerical range is a convex set or not. The result can be used to easily judge the locally perfect distinguishability of any two unitary operations $$U_1$$ U 1 and $$U_2$$ U 2 satisfying $$U_1^\dag U_2=V$$ U 1 † U 2 = V . Moreover, we design the corresponding protocol of local discrimination. Meanwhile, an interesting phenomenon is discovered: Under certain conditions with a single run, $$U_1$$ U 1 and $$U_2$$ U 2 such that $$U_1^\dag U_2=V$$ U 1 † U 2 = V are locally distinguishable with certainty if and only if they are perfectly distinguishable by global operations.

Journal

Quantum Information ProcessingSpringer Journals

Published: Nov 12, 2015

References

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