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Unmeasured Bohmian properties and their measurement through local-in-position weak values for assessing non-contextual quantum dynamics

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Albareda Piquer,  G.
Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona;
Institut de Química Teòrica i Computacional, Universitat de Barcelona;
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Pandey, D., Sampaio, R., Ala-Nissila, T., Albareda Piquer, G., & Oriols, X. (2019). Unmeasured Bohmian properties and their measurement through local-in-position weak values for assessing non-contextual quantum dynamics.


Abstract
We present a thorough discussion about the significance of unmeasured properties, defined in terms of Bohmian trajectories, to provide information on the dynamics of general quantum systems. We prove the existence of a one-to-one correspondence between any unmeasured Bohmian property and a local-in-position weak value of the corresponding observable. Consequently, as long as weak values are experimentally accessible, unmeasured Bohmian properties are measurable and always yield a positive semi-definite output value probability distribution. Importantly, while generalized (positive-operator valued) measurements of multi-time expectation values happen to be contextual, local-in-position weak values are, by construction, free from quantum backaction effects. Therefore, we conclude that unmeasured Bohmian properties, measurable through weak values, can be understood as a genuine representation of the intrinsic dynamics of quantum systems. The dwell time, the work distribution or the high-frequency electrical current of quantum systems are shown to be paradigmatic examples of the physical soundness of unmeasured Bohmian properties.