Dependence of measurement outcomes on the dynamics of quantum coherent interactions between the system and the meter

TL;DR

This paper explores how quantum measurement outcomes are influenced by the coherent dynamics of the system-meter interaction, revealing that measurement results are deeply connected to the quantum interference effects during back-action.

Contribution

It demonstrates that measurement outcomes depend on the quantum coherent back-action dynamics, linking physical property values to interference effects and the system's evolution.

Findings

Measurement outcomes depend on the quantum coherent back-action dynamics.

Weak values emerge from the Hamilton-Jacobi equation of back-action.

Eigenvalues arise from quantum interferences corresponding to Fourier transforms.

Abstract

Information about the internal properties of a system can only be obtained through interactions of the system with an external meter. However, such interactions generally result in entanglement between the system and the meter, making it difficult to trace the measurement result back to a specific value of the physical property in the system. It is therefore possible that the outcomes of quantum measurements depend in a non-trivial manner on the dynamics of the measurement interaction, possibly providing a physical explanation for the role of measurement contexts in quantum mechanics. Here, we show that the effects of the measurement interaction on the meter can be described entirely in terms of the quantum coherent system dynamics associated with the back-action on the system. For sufficiently small back-action uncertainties, the physical property of the system is described by a weak value obtained from the Hamilton-Jacobi equation of the back-action dynamics. At higher measurement resolutions, the observed values are determined by quantum interferences between different amounts of back-action. Eigenvalues emerge when the quantum interferences between different back-actions correspond to a Fourier transform in the back-action parameter. We conclude that the values of physical properties obtained in quantum measurements originate from the quantum coherent properties of the back-action dynamics generated by that physical property during an interaction. Measurement outcomes represent elements of the dynamics and cannot be explained by measurement independent elements of reality.