A relational perspective on the Wigner-Araki-Yanase theorem

Abstract

We present a novel interpretation of the Wigner-Araki-Yanase (WAY) theorem based on a relational view of quantum mechanics. Several models are analysed in detail, backed up by general considerations, which serve to illustrate that the moral of the WAY theorem may be that in the presence of symmetry, a measuring apparatus must fulfil the dual purpose of both reflecting the statistical behaviour of the system under investigation, and acting as a physical reference system serving to define those quantities which must be understood as relative.

Version 2 contains some corrections and improvements suggested by an anonymous referee

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Cited by in corpus (13)

• Quantum reference frame transformations as symmetries and the paradox of the third particle
• Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory
• Internal quantum reference frames for finite Abelian groups
• Operational Quantum Reference Frame Transformations
• Quantum measurements constrained by the third law of thermodynamics
• Entanglement-asymmetry correspondence for internal quantum reference frames
• Wigner-Araki-Yanase theorem for continuous and unbounded conserved observables
• Measurement disturbance and conservation laws in quantum mechanics
• Perspective-neutral approach to quantum frame covariance for general symmetry groups
• Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
• Classicality of the heat produced by quantum measurements
• A quantum reference frame size-accuracy trade-off for quantum channels
• Macroscopicity and observational deficit in states, operations, and correlations