Pointer-based simultaneous measurements of conjugate observables in a thermal environment

TL;DR

This paper models simultaneous measurements of conjugate observables in a thermal environment using pointer-based methods combined with quantum Brownian motion, providing a formal solution and new uncertainty bounds.

Contribution

It introduces a formal solution for measurement dynamics in quadratic Hamiltonians and extends uncertainty relations considering system squeezing.

Findings

Derived a lower bound for measurement uncertainty in noisy conditions

Extended existing uncertainty relations to include squeezing effects

Classified minimal uncertainty states in the context of thermal environments

Abstract

We combine traditional pointer-based simultaneous measurements of conjugate observables with the concept of quantum Brownian motion of multipartite systems to phenomenologically model simultaneous measurements of conjugate observables in a thermal environment. This approach provides us with a formal solution of the complete measurement dynamics for quadratic Hamiltonians and we can therefore discuss the measurement uncertainty and optimal measurement times. As a main result, we obtain a lower bound for the uncertainty of a noisy measurement, which is an extension of a previously known uncertainty relation and in which the squeezing of the system state to be measured plays an important role. This also allows us to classify minimal uncertainty states in more detail.