Measurement statistics and the dynamics of quantum processes

Quantum states are characterized by non-classical correlations between non-commuting properties, and these correlations are responsible for all experimentally observable effects studied in research on quantum mechanics. Quantum state tomography using weak measurements provides a particularly direct access to such non-classical correlations by representing them as experimentally observed complex conditional probabilities. Significantly, the imaginary part of this probability distribution is obtained from a dynamical response of the system. As I discuss here, this is no accident: non-commutativity itself should be understood as a identification of dynamics with complex-valued correlations. It may then be possible to explain all of quantum physics in terms of fundamental relations between physical properties given by the equations of motion that describe physical processes.

References:
[1] "On the role of complex phases in the quantum statistics of weak measurements," H. F. Hofmann, New J. Phys. 13, 103009 (2011).
[2] "Complex joint probabilities as expressions of reversible transformations in quantum mechanics," H. F. Hofmann, New J. Phys. 14, 043031 (2012).
[3] "Derivation of quantum mechanics from a single fundamental modification of the relations between physical properties," H. F. Hofmann, Phys. Rev. A 89, 042115 (2014).

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