Uncertainty relation for indirect measurement

TL;DR

This paper derives a new quantum measurement uncertainty relation for indirect measurements, linking thermodynamic activity and measurement noise, with implications for understanding quantum incompatibility and disturbance.

Contribution

It introduces a novel thermodynamic-based uncertainty relation for indirect quantum measurements, connecting survival activity and measurement noise.

Findings

Reciprocal relation between survival activity and measurement noise.

The uncertainty affects disturbance via a universal noise-disturbance relation.

Bridges quantum measurement uncertainty with thermodynamic concepts.

Abstract

Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate observables. While measurement uncertainty has been established for the accuracy of quantum measurement, thermodynamic uncertainty is being researched as a new perspective on the accuracy of fluctuating observables that trades off a physical cost in the classical or quantum regime. Following these ideas, we derive a new measurement uncertainty with respect to indirect measurement in the light of quantum thermodynamics. The obtained result shows a reciprocal relation between a survival activity, which is a frenetic contribution to the thermodynamic system, and noise due to the measurement approach. Moreover, this uncertainty can also affect the disturbance of an incompatible counterpart through the universal noise-disturbance relation.