On the estimation of interaction parameters in weak measurements

TL;DR

This paper investigates the relationship between weak measurement signal amplification and quantum measurement sensitivity, concluding that extreme weak values do not enhance sensitivity and can be seen as precise estimates of observables.

Contribution

It demonstrates that weak measurement amplification does not improve sensitivity and clarifies the interpretation of real weak values as precise estimates.

Findings

Extreme weak values do not improve measurement sensitivity.

All real weak values have the same sensitivity as eigenvalue measurements.

Weak values can be interpreted as precise, zero-uncertainty estimates.

Abstract

Since weak measurements are known to produce measurement values that can be much larger than the maximal eigenvalues of the measured observable, it is an interesting question how this enhancement of the measurement signal relates to the sensitivity of quantum measurements as investigated in the field of quantum metrology. In this presentation, it is pointed out that the estimation of a small interaction parameter using weak measurements actually corresponds to standard quantum metrology, where the logarithmic derivatives of the final measurement probabilities are proportional to the corresponding weak values. The analysis of the general weak measurement formalism then shows that extreme weak values do not improve the sensitivity. Instead, all final measurements with real weak values have the same sensitivity as a final measurement of the eigenvalues. This result supports the view that real weak values can be interpreted as precise, zero uncertainty estimates of a quantum observable, despite their deviation from the eigenvalues of the corresponding operator.