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Quantum rms error and Heisenberg’s error-disturbance relation

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JournalEPJ Web of Conferences
DatePublished - 2014
Volume78
Number of pages8
Original languageEnglish

Abstract

Reports on experiments recently performed in Vienna [Erhard et al, Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg’s error-disturbance relation. In contrast, a Heisenberg-type tradeoff relation for joint measurements of position and momentum has been formulated and proven in [Phys. Rev. Lett. 111, 160405 (2013)]. Here I show how the apparent conflict is resolved by a careful consideration of the quantum generalisation of the notion of root-mean-square error. The claim of a violation of Heisenberg’s principle fails as it is based on unsuitable measures of error and disturbance. An alternative, operationally significant, error measure enables the formulation of a new general trade-off relation for the necessary errors in approximate joint measurements of incompatible observables. This is illustrated for the case of qubit measurements. The experiments mentioned may directly be used to test this new error inequality.

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