Path integrals, the ABL rule and the three-box paradox

Sokolovski, D.; Gimenez, I. Puerto; Mayato, R. Sala

doi:10.1016/j.physleta.2008.07.074

Cited by 12 publications

(26 citation statements)

References 20 publications

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“…As P M1 (A|¬1) = P M2 (A|¬2) = 0, p 1 P M1 (A|1) = p 2 P M2 (A|2) = 1/9 and P N (A) = 1/9, this would give 0 ≥ 1/9 ≥ 2/9 and we have our contradictions (see also [SGM08] for a related analysis using path integrals).…”

Section: Non-invasivenessmentioning

confidence: 85%

Measurements, disturbances and the quantum three box paradox

Maroney

2017

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

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Quantum pre-and post-selection (PPS) paradoxes occur when counterfactual inferences are made about different measurements that might have been performed, between two measurements that are actually performed. The 3 box paradox is the paradigm example of such a paradox, where a ball is placed in one of three boxes and it is inferred that it would have been found, with certainty, both in box 1 and in box 2 had either box been opened on their own. Precisely what is at stake in PPS paradoxes has been unclear, and classical models have been suggested which are supposed to mimic the essential features of the problem. We show that the essential difference between the classical and quantum pre-and post-selection effects lies in the fact that for a quantum PPS paradox to occur the intervening measurement, had it been performed, would need to be invasive but non-detectable. This invasiveness is required even for null result measurements. While some quasi-classical features (such as non-contextuality and macrorealism) are compatible with PPS paradoxes, it seems no fully classical model of the 3 box paradox is possible.

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Section: Non-invasivenessmentioning

confidence: 85%

Measurements, disturbances and the quantum three box paradox

Maroney

2017

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

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“…Firstly, it should be remembered that Equation (38) expresses the average ξ defined in a standard way by Equation (20), in terms of the system's amplitudes α [i]. Secondly, as discussed in Section 8, the mean pointer reading in an accurate measurement of a projector yields the relative frequency with which the real path in question is traveled.…”

Section: Weak Values and The Uncertainty Principlementioning

confidence: 99%

Quantum Measurements, Stochastic Networks, the Uncertainty Principle, and the Not So Strange “Weak Values”

Sokolovski

2016

Mathematics

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Suppose we make a series of measurements on a chosen quantum system. The outcomes of the measurements form a sequence of random events, which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network connecting all possible outcomes. The paths are shaped from the virtual paths of the system, and the corresponding probabilities are determined by the measuring devices employed. If the measurements are highly accurate, the virtual paths become "real", and the mean values of a quantity (a functional) are directly related to the frequencies with which the paths are traveled. If the measurements are highly inaccurate, the mean (weak) values are expressed in terms of the relative probabilities' amplitudes. For pre-and post-selected systems they are bound to take arbitrary values, depending on the chosen transition. This is a direct consequence of the uncertainty principle, which forbids one from distinguishing between interfering alternatives, while leaving the interference between them intact.

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“…1). Rather, in accordance with the Uncertainty Principle [15], [20], they are combined into two real routes, with amplitudes,…”

Section: Accurate (Strong) Measurementsmentioning

confidence: 99%

“…The Uncertainty Principle may warn us against such an attempt [6], [20], but we want to proceed anyway, by making the measurement highly inaccurate, or weak. We send ∆f → ∞, so that the r.h.s of…”

Section: Inaccurate (Weak) Measurementsmentioning

confidence: 99%

“…The " quantum Cheshire cat paradox", as well as other counterfactual quantum "paradoxes" [24], [25], [26] are easily dismissed if one is content to see a quantum system as a "toolbox" from which one may assemble different classical statistical ensembles by performing different measurements at different times [20]. As yet another example of this kind, consider the "3-box" case [23], [24], where a three-state system can reach the final state via three routes defined by intermediate projections on three states |i , i = 1, 2, 3.…”

Section: Weak Measurements and Counterfactual Statementsmentioning

confidence: 99%

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Weak measurements measure probability amplitudes (and very little else)

Sokolovski

2016

Physics Letters A

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Conventional quantum mechanics describes a pre-and post-selected system in terms of virtual (Feynman) paths via which the final state can be reached. In the absence of probabilities, a weak measurement (WM) determines the probability amplitudes for the paths involved. The weak values (VW) can be identified with these amplitudes, or their linear combinations. This allows us to explain the "unusual" properties of the VW, and avoid the "paradoxes" often associated with the WM.

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Path integrals, the ABL rule and the three-box paradox

Cited by 12 publications

References 20 publications

Measurements, disturbances and the quantum three box paradox

Measurements, disturbances and the quantum three box paradox

Quantum Measurements, Stochastic Networks, the Uncertainty Principle, and the Not So Strange “Weak Values”

Weak measurements measure probability amplitudes (and very little else)

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