Experimental test of the tradeoff relation in weak measurement

TL;DR

This paper experimentally verifies a theoretical tradeoff relation between information gain and reversibility in weak measurements using polarization-encoded photons, providing a universal characterization tool for weak measurement processes.

Contribution

It experimentally confirms the theoretical tradeoff relation in qubit systems and demonstrates a complete traversal of weak measurement operators.

Findings

Experimental verification of the tradeoff relation.

Complete traversal of weak measurement operators achieved.

Mapping to the upper bound of the tradeoff relation obtained.

Abstract

An upper bound between the information gain and state reversibility of weak measurement was first developed by Y. K. Cheong and S. W. Lee [Phys. Rev. Lett. 109, 150402 (2012)]. Their results are valid for arbitrary d-level quantum systems. In light of the commonly used qubit system in quantum information, a sharp tradeoff relation can be obtained. In this letter, this tradeoff relation is experimentally verified with polarization encoded single photons from a quantum dot. Furthermore, a complete traversal of weak measurement operators is realized, and the mapping to the least upper bound of this tradeoff relation is obtained. Our results complement the theoretical work and provide a universal ruler for the characterization of weak measurements.