Hardy's Paradox and Measurement-disturbance Relations

TL;DR

This paper links Hardy's paradox to measurement-disturbance relations, showing how their interplay explains the inconsistency with local realism and simplifies experimental tests involving entanglement and non-commuting measurements.

Contribution

It establishes a quantitative relation between Hardy's paradox and measurement-disturbance relations, clarifying the role of conditional measurements in local realism violations.

Findings

Hardy's paradox relates to measurement-disturbance breaking.

Simplified experimental test of local realism proposed.

Analysis enhances understanding of entanglement and measurement disturbance.

Abstract

We establish a quantitative relation between Hardy's paradox and the breaking of uncertainty principle in the sense of measurement-disturbance relations in the conditional measurement of non-commuting operators. The analysis of the inconsistency of local realism with entanglement by Hardy is simplified if this breaking of measurement-disturbance relations is taken into account, and a much simplified experimental test of local realism is illustrated in the framework of Hardy's thought experiment. The essence of Hardy's model is identified as a combination of two conditional measurements, which give rise to definite eigenvalues to two non-commuting operators simultaneously in hidden-variables models. Better understanding of the intimate interplay of entanglement and measurement-disturbance is crucial in the current discussions of Hardy's paradox using the idea of weak measurement, which is based on a general analysis of measurement-disturbance relations.