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Title: Quantum averages of weak values

Abstract

We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a definite mechanical effect on a measuring probe specifically designed to minimize the back reaction on the measured system. We then present an interesting framework for general measurement conditions (where the back reaction on the system may not be negligible) in which the measurement outcomes can still be interpreted as quantum averages of weak values. We show that in the classical limit, there is a direct correspondence between quantum averages of weak values and posterior expectation values of classical dynamical properties according to the classical inference framework.

Authors:
 [1];  [2];  [3];  [4];  [5]
  1. Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208 (United States)
  2. (Israel)
  3. (United States)
  4. Department of Physics and Astronomy, University of South Carolina, Columbia, SC 29208 (United States)
  5. (Colombia)
Publication Date:
OSTI Identifier:
20786447
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052111; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; CLASSICAL MECHANICS; ENERGY LEVELS; PROBES; QUANTUM MECHANICS; QUANTUM OPERATORS

Citation Formats

Aharonov, Yakir, Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, Botero, Alonso, and Departamento de Fisica, Universidad de Los Andes, Apartado Aereo 4976, Bogota. Quantum averages of weak values. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Aharonov, Yakir, Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, Botero, Alonso, & Departamento de Fisica, Universidad de Los Andes, Apartado Aereo 4976, Bogota. Quantum averages of weak values. United States. doi:10.1103/PHYSREVA.72.0.
Aharonov, Yakir, Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, Botero, Alonso, and Departamento de Fisica, Universidad de Los Andes, Apartado Aereo 4976, Bogota. Tue . "Quantum averages of weak values". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786447,
title = {Quantum averages of weak values},
author = {Aharonov, Yakir and Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978 and Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030 and Botero, Alonso and Departamento de Fisica, Universidad de Los Andes, Apartado Aereo 4976, Bogota},
abstractNote = {We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a definite mechanical effect on a measuring probe specifically designed to minimize the back reaction on the measured system. We then present an interesting framework for general measurement conditions (where the back reaction on the system may not be negligible) in which the measurement outcomes can still be interpreted as quantum averages of weak values. We show that in the classical limit, there is a direct correspondence between quantum averages of weak values and posterior expectation values of classical dynamical properties according to the classical inference framework.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
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