Complex joint probabilities as expressions of reversible transformations in quantum mechanics

Hofmann Holger Friedrich

New Journal of Physics

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex conditional probabilities that describe the fundamental relation between precise statements about the three different observables. Since such transformations merely change the representation of the quantum state, these conditional probabilities provide a state-independent definition of the reversible and therefore effectively deterministic relations between the outcomes of different quantum measurements, including measurements of the same property performed at different times. In this paper, it is shown how classical reality emerges as an approximation to the fundamental laws of quantum determinism expressed by complex conditional probabilities. The quantum mechanical origin of phase spaces and trajectories is identified and implications for the interpretation of quantum measurements are considered. It is argued that the transformation laws of quantum determinism provide a fundamental description of the measurement dependence of empirical reality.

Weak Measurements

Entangled States

Physics [ 420 ]

eng

Iop Publishing Led

(c) 2013 IOP Publishing

[ISSN] 1367-2630

[DOI] 10.1088/1367-2630/14/4/043031

[DOI] http://dx.doi.org/10.1088/1367-2630/14/4/043031