Weak values and consistent histories in quantum theory |
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| Institution: | 1. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;2. Collaborative Innovation Center of Quantum Matter, Beijing 100190, China;3. School of Physics, Peking University, Beijing 100871, China;1. Division of Cardiology, Faculty of Medicine, Geneva University Hospitals, Geneva, Switzerland;2. Department of Ambulatory and Community Medicine, University of Lausanne, Lausanne, Switzerland;3. Department of Cardiology, University Hospital Bern, Bern, Switzerland;4. Department of Cardiology, University Heart Center, Zürich, Switzerland;5. Department of General Internal Medicine, University of Bern, Bern, Switzerland;6. Department of Cardiology, Lausanne University Hospital, Lausanne, Switzerland |
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| Abstract: | A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that “strange” weak values for projection operators (such as values less than zero) always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application of Lüders’ Rule. It is argued that an assumption of reverse causality (a form of time symmetry) implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterized as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions. |
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