Relation between strength of interaction and accuracy of measurement for a quantum measurement

TL;DR

This paper investigates how the interaction strength and timing affect the accuracy of quantum measurements, revealing that non-commuting interactions are essential for error-free measurements of certain observables.

Contribution

It establishes a formal relationship between interaction strength, measurement duration, and accuracy, highlighting the importance of non-commuting Hamiltonians for error-free quantum measurements.

Findings

Non-trivial relationship among interaction strength, time, and measurement accuracy.

Error-free measurement requires the interaction Hamiltonian not to commute with the system Hamiltonian.

Provides Hamiltonian formalism-based conditions for precise quantum measurements.

Abstract

The process of measuring a two-level quantum system was examined by applying Hamiltonian formalism. For the measurement of an observable that does not commute with the system Hamiltonian, a non-trivial relationship among the strength of interaction, the time interval of the process, and the accuracy of the measurement was obtained. Particularly, to achieve an error-free measurement of such an observable, a condition stating that the interaction Hamiltonian does not commute with the system Hamiltonian needs to be satisfied.