Optimal unambiguous discrimination of pure qudits

Optimal unambiguous discrimination of pure qudits Linearly independent pure quantum states can be discriminated unambiguously, while linearly dependent states cannot. We use a physical accessible unitary transformation to map the nonorthogonal quantum states onto a set of orthogonal ones so that measuring the output states can discriminate the initial states with the deterministic and inconclusive results. The failure states that give an inconclusive result are linearly dependent ones. In finding the optimal unambiguous discrimination (UD), we show that a main constraint condition that the determinant constructed by the complex inner products of the failure states must be zero, along with two additional conditions, can provide solutions to the problem of the optimal UD for pure qudits. For any d, we give one analytical solution as all the Berry phases being zero. We also derive the lowest bound of the total failure probability of the optimal UD. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Optimal unambiguous discrimination of pure qudits

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Publisher
Springer US
Copyright
Copyright © 2013 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/s11128-013-0666-x
Publisher site
See Article on Publisher Site

Abstract

Linearly independent pure quantum states can be discriminated unambiguously, while linearly dependent states cannot. We use a physical accessible unitary transformation to map the nonorthogonal quantum states onto a set of orthogonal ones so that measuring the output states can discriminate the initial states with the deterministic and inconclusive results. The failure states that give an inconclusive result are linearly dependent ones. In finding the optimal unambiguous discrimination (UD), we show that a main constraint condition that the determinant constructed by the complex inner products of the failure states must be zero, along with two additional conditions, can provide solutions to the problem of the optimal UD for pure qudits. For any d, we give one analytical solution as all the Berry phases being zero. We also derive the lowest bound of the total failure probability of the optimal UD.

Journal

Quantum Information ProcessingSpringer Journals

Published: Nov 7, 2013

References

  • Quantum state discrimination
    Barnett, S.M.; Croke, S.
  • Overlap and distinguishability of quantum states
    Dieks, D

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