Strong correspondence principle for joint measurement of conjugate observables

TL;DR

This paper extends the Ehrenfest correspondence principle to joint measurements of conjugate variables in quantum mechanics, showing that their statistics resemble classical equations when using Wigner functions and accounting for detector interactions.

Contribution

It introduces the strong correspondence principle, linking quantum joint measurement statistics to classical equations via Wigner functions and detector effects.

Findings

Quantum joint measurement statistics mirror classical equations with Wigner functions.

Detectors add an additive term to cumulants, affecting measurement outcomes.

Gaussian detectors influence only the first and second cumulants.

Abstract

It is demonstrated that the the statistics for a joint measurement of two conjugate variables in Quantum Mechanics are expressed through an equation identical to the classical one, provided that joint classical probabilities are substituted by Wigner functions and that the interaction between system and detectors is accounted for. This constitutes an extension of Ehrenfest correspondence principle, and it is thereby dubbed strong correspondence principle. Furthermore, it is proved that the detectors provide an additive term to all the cumulants, and that if they are prepared in a Gaussian state they only contribute to the first and second cumulant.