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arXiv · 1412.7609

Hardy's Paradox and Measurement-disturbance Relations

Kazuo Fujikawa·C. H. Oh·Sixia Yu
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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.

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Kazuo Fujikawa, C. H. Oh, Sixia Yu. 2014-12-24. Hardy's Paradox and Measurement-disturbance Relations. https://doi.org/10.1103/physreva.91.012105

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