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Title: Approximating incompatible von Neumann measurements simultaneously

Abstract

We study the problem of performing orthogonal qubit measurements simultaneously. Since these measurements are incompatible, one has to accept additional imprecision. An optimal joint measurement is the one with the least possible imprecision. All earlier considerations of this problem have concerned only joint measurability of observables, while in this work we also take into account conditional state transformations (i.e., instruments). We characterize the optimal joint instrument for two orthogonal von Neumann instruments as being the Lueders instrument of the optimal joint observable.

Authors:
 [1];  [1];  [2];  [2]
  1. Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark)
  2. Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia)
Publication Date:
OSTI Identifier:
21448666
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 82; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.82.032328; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENERGY LEVELS; QUANTUM MECHANICS; QUANTUM STATES; QUBITS; TRANSFORMATIONS; INFORMATION; MECHANICS; QUANTUM INFORMATION

Citation Formats

Heinosaari, Teiko, Jivulescu, Maria Anastasia, Department of Mathematics, University Politehnica Timisoara, P-ta Victoriei Nr. 2, R-300006 Timisoara, Reitzner, Daniel, Ziman, Mario, and Faculty of Informatics, Masaryk University, Botanicka 68a, Brno. Approximating incompatible von Neumann measurements simultaneously. United States: N. p., 2010. Web. doi:10.1103/PHYSREVA.82.032328.
Heinosaari, Teiko, Jivulescu, Maria Anastasia, Department of Mathematics, University Politehnica Timisoara, P-ta Victoriei Nr. 2, R-300006 Timisoara, Reitzner, Daniel, Ziman, Mario, & Faculty of Informatics, Masaryk University, Botanicka 68a, Brno. Approximating incompatible von Neumann measurements simultaneously. United States. https://doi.org/10.1103/PHYSREVA.82.032328
Heinosaari, Teiko, Jivulescu, Maria Anastasia, Department of Mathematics, University Politehnica Timisoara, P-ta Victoriei Nr. 2, R-300006 Timisoara, Reitzner, Daniel, Ziman, Mario, and Faculty of Informatics, Masaryk University, Botanicka 68a, Brno. 2010. "Approximating incompatible von Neumann measurements simultaneously". United States. https://doi.org/10.1103/PHYSREVA.82.032328.
@article{osti_21448666,
title = {Approximating incompatible von Neumann measurements simultaneously},
author = {Heinosaari, Teiko and Jivulescu, Maria Anastasia and Department of Mathematics, University Politehnica Timisoara, P-ta Victoriei Nr. 2, R-300006 Timisoara and Reitzner, Daniel and Ziman, Mario and Faculty of Informatics, Masaryk University, Botanicka 68a, Brno},
abstractNote = {We study the problem of performing orthogonal qubit measurements simultaneously. Since these measurements are incompatible, one has to accept additional imprecision. An optimal joint measurement is the one with the least possible imprecision. All earlier considerations of this problem have concerned only joint measurability of observables, while in this work we also take into account conditional state transformations (i.e., instruments). We characterize the optimal joint instrument for two orthogonal von Neumann instruments as being the Lueders instrument of the optimal joint observable.},
doi = {10.1103/PHYSREVA.82.032328},
url = {https://www.osti.gov/biblio/21448666}, journal = {Physical Review. A},
issn = {1050-2947},
number = 3,
volume = 82,
place = {United States},
year = {Wed Sep 15 00:00:00 EDT 2010},
month = {Wed Sep 15 00:00:00 EDT 2010}
}