Quantum Weak Values and Logic : An Uneasy Couple
(2017) In Foundations of Physics 47(3). p.430452 Abstract
Quantum mechanical weak values of projection operators have been used to answer whichway 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 threebox 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 whichway 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 threebox 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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 author
 Svensson, Bengt E Y ^{LU}
 organization
 publishing date
 201703
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Hardy’s paradox, Logic, Quantum measurement, Quantum pigeonhole principle, Threebox problem, Weak values
 in
 Foundations of Physics
 volume
 47
 issue
 3
 pages
 430  452
 publisher
 Springer
 external identifiers

 wos:000394980200006
 scopus:85011716032
 ISSN
 00159018
 DOI
 10.1007/s1070101700685
 language
 English
 LU publication?
 yes
 id
 e01dc25d0483480192bd8ae1414cb4bf
 date added to LUP
 20170220 09:47:01
 date last changed
 20241014 00:29:53
@article{e01dc25d0483480192bd8ae1414cb4bf, abstract = {{<p>Quantum mechanical weak values of projection operators have been used to answer whichway 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 threebox 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 = {{00159018}}, keywords = {{Hardy’s paradox; Logic; Quantum measurement; Quantum pigeonhole principle; Threebox problem; Weak values}}, language = {{eng}}, number = {{3}}, pages = {{430452}}, publisher = {{Springer}}, series = {{Foundations of Physics}}, title = {{Quantum Weak Values and Logic : An Uneasy Couple}}, url = {{http://dx.doi.org/10.1007/s1070101700685}}, doi = {{10.1007/s1070101700685}}, volume = {{47}}, year = {{2017}}, }