Foundations and applications of weak quantum measurements

Aharonov, Yakir; Cohen, Eliahu; Elitzur, Avshalom C.

doi:10.1103/physreva.89.052105

Cited by 81 publications

(115 citation statements)

References 30 publications

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“…[2,3] for reviews and further references. 1 It is also the view taken in the approach by Aharonov and his many collaborators, starting with paper [4] (in the sequel referred to as ABL) and continuing in the development of the concepts of weak measurements and weak values [5]; for some reviews see [6][7][8][9][10][11][12]. In this paper, I shall mostly follow this line of thought of Aharonov and collaborators.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Weak Values and Logic: An Uneasy Couple

Svensson

2017

Found Phys

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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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Section: Introductionmentioning

confidence: 99%

“…A basic one is that a weak value does indeed involve an incoming, preselected, state |in as well as a final, postselected state | f for the system under investigation [5][6][7][8][9][10][11][12]. The interest is then focused on what may be said regarding the system at an intermediate time, i.e.…”

Section: Introductionmentioning

confidence: 99%

Quantum Weak Values and Logic: An Uneasy Couple

Svensson

2017

Found Phys

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“…8 I now turn to how the TTI relates to three key topics: hidden variables, nonlocality and determinism.…”

Section: The Interpretation Of φ|mentioning

confidence: 99%

“…7 Note, however, that it is possible, according to [8], to perform a weak measurement on a single particle, where all measurement results are used. My thanks to an anonymous referee for bringing this example to my attention.…”

Section: The Interpretation Of φ|mentioning

confidence: 99%

Can the two-time interpretation of quantum mechanics solve the measurement problem?

Robertson

2017

Studies in History and Philosophy of Science Part B: Studies in

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Over many years, Aharonov and co-authors have proposed a new interpretation of quantum mechanics: the two-time interpretation. This interpretation assigns two wavefunctions to a system, one of which propagates forwards in time and the other backwards. In this paper, I argue that this interpretation does not solve the measurement problem. In addition, I argue that it is neither necessary nor sufficient to attribute causal power to the backwards-evolving wavefunction Φ| and thus its existence should be denied, contra the two-time interpretation. Finally, I follow Vaidman in giving an epistemological reading of Φ|.

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“…Weak measurements are based on the von Neumann scheme for performing quantum measurements, albeit with a very small coupling compared to the measurement's uncertainty. The weak coupling created between the measured system and the measuring (quantum) pointer does not change significantly the measured state, yet provides robust information when an ensemble of states in discussed [9,10]. Given an operator A we wish to measure on a system |ψ , the coupling to the measuring pointer is achieved through the Hamiltonian…”

Section: Introductionmentioning

confidence: 99%

Weak Values and Quantum Nonlocality

Aharonov

Cohen

2016

Quantum Nonlocality and Reality

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Entanglement and nonlocality are studied in the framework of pre-/postselected ensembles with the aid of weak measurements and the Two-StateVector Formalism. In addition to the EPR-Bohm experiment, we revisit the Hardy and Cheshire Cat experiments, whose entangled pre-or post-selected states give rise to curious phenomena. We then turn to even more peculiar phenomenon suggesting "emerging correlations" between independent preand post-selected ensembles of particles. This can be viewed as a quantum violation of the classical "pigeonhole principle".

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Foundations and applications of weak quantum measurements

Cited by 81 publications

References 30 publications

Quantum Weak Values and Logic: An Uneasy Couple

Quantum Weak Values and Logic: An Uneasy Couple

Can the two-time interpretation of quantum mechanics solve the measurement problem?

Weak Values and Quantum Nonlocality

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