The minimum-error discrimination via Helstrom family of ensembles and convex optimization

  • Authors:

  • M. A. Jafarizadeh;Y. Mazhari;M. Aali

  • Affiliations:

  • Department of Theoretical Physics and Astrophysics, University of Tabriz, Tabriz, Iran 51664 and Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran 19395-1795 and Research ...;Department of Theoretical Physics and Astrophysics, University of Tabriz, Tabriz, Iran 51664;Department of Physics, Faculty of Science, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran 53714-161

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2011

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Abstract

Using the convex optimization method and Helstrom family of ensembles introduced in Ref. Kimura et al. in Phys Rev A, 79:062306 (2009), we discuss optimal ambiguous discrimination in qubit systems for N known quantum states. We obtain optimal success probability (OSP) and optimal measurement (OM) for N(驴 4) known equiprobable quantum states where all these states are distributed at the same distance from the center of Bloch ball which all the states do not lie on the same plane. After reproducing known results for distinguishing between two quantum states, we also exactly discuss discrimination of three quantum state where OSP and OM are calculated explicitly. In particular examples of three states, for a numerical case, mirror symmetric states, and particularly chosen coplanar pure states, previously obtained results are reproduced. We also obtain OSP and OM for a particular case of states considered on the line, circumference of a circle, and states that is defined by vertices of a Platonic solid. In addition, OSP is presented for a special case of four states.