State distinguishability under weak measurement and post-selection: A unified system and device perspective

TL;DR

This paper analyzes the trade-offs in quantum state distinguishability using weak measurements and post-selection, revealing that combined techniques can reduce disturbance while maintaining sensitivity, with implications for quantum measurement precision.

Contribution

It provides a unified framework quantifying the disturbance and distinguishability in weak measurements with post-selection, highlighting conditions for reduced system disturbance and improved measurement sensitivity.

Findings

Weak measurement alone does not reduce disturbance significantly.

Post-selection combined with weak measurement improves sensitivity and reduces disturbance.

Exact post-selection probability is higher under realistic conditions than approximate models.

Abstract

We quantify the disturbance of a quantum state undergoing a sequence of observations, and particularly focus on a weak measurement followed by post-selection and compare these results to the projective counterpart. Taking into account the distinguishability of both, the system and the device, we obtain the exact trade-off between the system state disturbance and the change of the device pointer state. We show that for particular post-selection procedures the coupling strength between the system and the device can be significantly reduced without loosing measurement sensitivity, which is directly transferred to a reduced state disturbance of the system. We observe that a weak measurement alone does not provide this advantage but only in combination with post-selection a significant improvement in terms of increased measurement sensitivity and reduced state disturbance is found. We further show that under realistic experimental conditions this state disturbance is small, whereas the exact post-selection probability is considerably larger than the approximate value given by the overlap of the initial and final state when neglecting the system state disturbance.