Direct Characterization of Quantum Measurements using Weak Values

TL;DR

This paper introduces a method for directly characterizing quantum measurement devices using a time-symmetric weak measurement formalism, applicable at any measurement strength, with experimental validation.

Contribution

It proposes a novel protocol for direct tomography of measurement apparatuses based on the backward weak measurement formalism, enhancing accuracy and generality.

Findings

Protocol works with arbitrary measurement strength

Experimental demonstration validates the method

Improved accuracy by considering measurement completeness

Abstract

The time-symmetric formalism endows the weak measurement and its outcome, the weak value,many unique features. In particular, it allows a direct tomography of quantum states without resort to complicated reconstruction algorithms and provides an operational meaning to wave functions and density matrices. Here, we propose and experimentally demonstrate the direct tomography of a measurement apparatus by taking the backward direction of weak measurement formalism. Our protocol works rigorously with the arbitrary measurement strength, which offers an improved accuracy and precision. The precision can be further improved by taking into account the completeness condition of the measurement operators, which also ensures the feasibility of our protocol for the characterization of the arbitrary quantum measurement. Our work provides new insight on the symmetry between quantum states and measurements, as well as an efficient method to characterize a measurement apparatus.