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Title: Implementing nonprojective measurements via linear optics: An approach based on optimal quantum-state discrimination

Abstract

We discuss the problem of implementing generalized measurements [positive operator-valued measures (POVMs)] with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an optimization problem for a chosen cost function. We formulate a general principle: the implementation is only possible if a linear-optics circuit exists for which the quantum mechanical optimum (minimum) is still attainable after dephasing the corresponding quantum states. The general principle enables us, for instance, to derive a set of necessary conditions for the linear-optics implementation of the POVM that realizes the quantum mechanically optimal unambiguous discrimination of two pure nonorthogonal states. This extends our previous results on projection measurements and the exact discrimination of orthogonal states.

Authors:
;  [1];  [1]; ;  [2]
  1. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430 (Japan)
  2. Quantum Information Theory Group, Institute of Theoretical Physics I, Institute of Optics, Information and Photonics (Max-Planck Forschungsgruppe), Universitaet Erlangen-Nuernberg, Staudtstr. 7, D-91058 Erlangen (Germany)
Publication Date:
OSTI Identifier:
20787466
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.73.062320; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; DATA TRANSMISSION; INFORMATION THEORY; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; OPTICS; OPTIMIZATION; QUANTUM MECHANICS

Citation Formats

Loock, Peter van, Nemoto, Kae, Munro, William J, Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS34 8QZ, Raynal, Philippe, and Luetkenhaus, Norbert. Implementing nonprojective measurements via linear optics: An approach based on optimal quantum-state discrimination. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Loock, Peter van, Nemoto, Kae, Munro, William J, Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS34 8QZ, Raynal, Philippe, & Luetkenhaus, Norbert. Implementing nonprojective measurements via linear optics: An approach based on optimal quantum-state discrimination. United States. https://doi.org/10.1103/PHYSREVA.73.0
Loock, Peter van, Nemoto, Kae, Munro, William J, Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS34 8QZ, Raynal, Philippe, and Luetkenhaus, Norbert. 2006. "Implementing nonprojective measurements via linear optics: An approach based on optimal quantum-state discrimination". United States. https://doi.org/10.1103/PHYSREVA.73.0.
@article{osti_20787466,
title = {Implementing nonprojective measurements via linear optics: An approach based on optimal quantum-state discrimination},
author = {Loock, Peter van and Nemoto, Kae and Munro, William J and Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS34 8QZ and Raynal, Philippe and Luetkenhaus, Norbert},
abstractNote = {We discuss the problem of implementing generalized measurements [positive operator-valued measures (POVMs)] with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an optimization problem for a chosen cost function. We formulate a general principle: the implementation is only possible if a linear-optics circuit exists for which the quantum mechanical optimum (minimum) is still attainable after dephasing the corresponding quantum states. The general principle enables us, for instance, to derive a set of necessary conditions for the linear-optics implementation of the POVM that realizes the quantum mechanically optimal unambiguous discrimination of two pure nonorthogonal states. This extends our previous results on projection measurements and the exact discrimination of orthogonal states.},
doi = {10.1103/PHYSREVA.73.0},
url = {https://www.osti.gov/biblio/20787466}, journal = {Physical Review. A},
issn = {1050-2947},
number = 6,
volume = 73,
place = {United States},
year = {Thu Jun 15 00:00:00 EDT 2006},
month = {Thu Jun 15 00:00:00 EDT 2006}
}