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Quantum Weak Values and Logic : An Uneasy Couple

Svensson, Bengt E Y LU (2017) In Foundations of Physics 47(3). p.430-452
Abstract

Quantum mechanical weak values of projection operators have been used to answer which-way questions, e.g. to trace which arms in a multiple Mach–Zehnder setup a particle may have traversed from a given initial to a prescribed final state. I show that this procedure might lead to logical inconsistencies in the sense that different methods used to answer composite questions, like “Has the particle traversed the way X or the way Y?”, may result in different answers depending on which methods are used to find the answer. I illustrate the problem by considering some examples: the “quantum pigeonhole” framework of Aharonov et al., the three-box problem, and Hardy’s paradox. To prepare the ground for my main conclusion on the incompatibility... (More)

Quantum mechanical weak values of projection operators have been used to answer which-way questions, e.g. to trace which arms in a multiple Mach–Zehnder setup a particle may have traversed from a given initial to a prescribed final state. I show that this procedure might lead to logical inconsistencies in the sense that different methods used to answer composite questions, like “Has the particle traversed the way X or the way Y?”, may result in different answers depending on which methods are used to find the answer. I illustrate the problem by considering some examples: the “quantum pigeonhole” framework of Aharonov et al., the three-box problem, and Hardy’s paradox. To prepare the ground for my main conclusion on the incompatibility in certain cases of weak values and logic, I study the corresponding situation for strong/projective measurements. In this case, no logical inconsistencies occur provided one is always careful in specifying exactly to which ensemble or sample space one refers. My results cast doubts on the utility of quantum weak values in treating cases like the examples mentioned.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Hardy’s paradox, Logic, Quantum measurement, Quantum pigeonhole principle, Three-box problem, Weak values
in
Foundations of Physics
volume
47
issue
3
pages
430 - 452
publisher
Springer
external identifiers
  • scopus:85011716032
  • wos:000394980200006
ISSN
0015-9018
DOI
10.1007/s10701-017-0068-5
language
English
LU publication?
yes
id
e01dc25d-0483-4801-92bd-8ae1414cb4bf
date added to LUP
2017-02-20 09:47:01
date last changed
2018-02-19 00:37:44
@article{e01dc25d-0483-4801-92bd-8ae1414cb4bf,
  abstract     = {<p>Quantum mechanical weak values of projection operators have been used to answer which-way questions, e.g. to trace which arms in a multiple Mach–Zehnder setup a particle may have traversed from a given initial to a prescribed final state. I show that this procedure might lead to logical inconsistencies in the sense that different methods used to answer composite questions, like “Has the particle traversed the way X or the way Y?”, may result in different answers depending on which methods are used to find the answer. I illustrate the problem by considering some examples: the “quantum pigeonhole” framework of Aharonov et al., the three-box problem, and Hardy’s paradox. To prepare the ground for my main conclusion on the incompatibility in certain cases of weak values and logic, I study the corresponding situation for strong/projective measurements. In this case, no logical inconsistencies occur provided one is always careful in specifying exactly to which ensemble or sample space one refers. My results cast doubts on the utility of quantum weak values in treating cases like the examples mentioned.</p>},
  author       = {Svensson, Bengt E Y},
  issn         = {0015-9018},
  keyword      = {Hardy’s paradox,Logic,Quantum measurement,Quantum pigeonhole principle,Three-box problem,Weak values},
  language     = {eng},
  number       = {3},
  pages        = {430--452},
  publisher    = {Springer},
  series       = {Foundations of Physics},
  title        = {Quantum Weak Values and Logic : An Uneasy Couple},
  url          = {http://dx.doi.org/10.1007/s10701-017-0068-5},
  volume       = {47},
  year         = {2017},
}