Measuring average of non-Hermitian operator with weak value in a Mach-Zehnder interferometer

TL;DR

This paper demonstrates a novel interferometric method to directly measure the weak value and average of non-Hermitian operators using a Mach-Zehnder interferometer, eliminating the need for weak measurement or post-selection.

Contribution

The authors introduce a new technique to measure weak values of non-Hermitian operators directly through interference visibility and phase shift, bypassing traditional weak measurement procedures.

Findings

Successful experimental demonstration with laser sources

Direct measurement of weak value without post-selection

Potential for technological applications in quantum measurement

Abstract

Quantum theory allows direct measurement of the average of a non-Hermitian operator using the weak value of the positive semidefinite part of the non-Hermitian operator. Here, we experimentally demonstrate the measurement of weak value and average of non-Hermitian operators by a novel interferometric technique. Our scheme is unique as we can directly obtain the weak value from the interference visibility and the phase shift in a Mach Zehnder interferometer without using any weak measurement or post selection. Both the experiments discussed here were performed with laser sources, but the results would be the same with average statistics of single photon experiments. Thus, the present experiment opens up the novel possibility of measuring weak value and the average value of non-Hermitian operator without weak interaction and post-selection, which can have several technological applications.