Measurement disturbance and conservation laws in quantum mechanics

Author:

Mohammady M. Hamed12,Miyadera Takayuki3,Loveridge Leon4

Affiliation:

1. QuIC, École Polytechnique de Bruxelles, CP 165/59, Université Libre de Bruxelles, 1050 Brussels, Belgium

2. RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava 84511, Slovakia

3. Department of Nuclear Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8540, Japan

4. Quantum Technology Group, Department of Science and Industry Systems, University of South-Eastern Norway, 3616 Kongsberg, Norway

Abstract

Measurement error and disturbance, in the presence of conservation laws, are analysed in general operational terms. We provide novel quantitative bounds demonstrating necessary conditions under which accurate or non-disturbing measurements can be achieved, highlighting an interesting interplay between incompatibility, unsharpness, and coherence. From here we obtain a substantial generalisation of the Wigner-Araki-Yanase (WAY) theorem. Our findings are further refined through the analysis of the fixed-point set of the measurement channel, some extra structure of which is characterised here for the first time.

Funder

European Union

Slovak Academy of Sciences

Japan Society for the Promotion of Science

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

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