Measuring measurement--disturbance relationships with weak values

TL;DR

This paper demonstrates that Ozawa's measurement--disturbance quantities can be experimentally determined using weak values, illustrating the failure of Heisenberg's original relation and supporting Ozawa's alternative formulation.

Contribution

It introduces an experimental method to measure Ozawa's quantities without prior knowledge, using weak-valued probabilities, and proposes a three-qubit experiment to test the relations.

Findings

Ozawa's quantities can be experimentally determined via weak values.

Heisenberg's original measurement--disturbance relation is shown to be false.

An alternative relation by Ozawa is validated through proposed experiment.

Abstract

Using formal definitions for measurement precision {\epsilon} and disturbance (measurement backaction) {\eta}, Ozawa [Phys. Rev. A 67, 042105 (2003)] has shown that Heisenberg's claimed relation between these quantities is false in general. Here we show that the quantities introduced by Ozawa can be determined experimentally, using no prior knowledge of the measurement under investigation --- both quantities correspond to the root-mean-squared difference given by a weak-valued probability distribution. We propose a simple three-qubit experiment which would illustrate the failure of Heisenberg's measurement--disturbance relation, and the validity of an alternative relation proposed by Ozawa.