'Measurement of Quantum Mechanical Operators' Revisited

TL;DR

This paper revisits the Wigner-Araki-Yanase theorem, clarifying its assumptions, exploring generalizations, and transforming it from a strict no-go result into a quantitative constraint on measurement accuracy in quantum mechanics.

Contribution

It provides a detailed analysis of the WAY theorem's assumptions, discusses its extensions, and shows how it can be viewed as a quantitative constraint on measurement precision.

Findings

Clarified the assumptions underlying the WAY theorem

Demonstrated how the theorem extends to approximate measurements

Reinterpreted the theorem as a quantitative constraint on measurement accuracy

Abstract

The Wigner-Araki-Yanase (WAY) theorem states a remarkable limitation to quantum mechanical measurements in the presence of additive conserved quantities. Discovered by Wigner in 1952, this limitation is known to induce constraints on the control of individual quantum systems in the context of information processing. It is therefore important to understand the precise conditions and scope of the WAY theorem. Here we elucidate its crucial assumptions, briefly review some generalizations, and show how a particular extension can already be obtained by a simple modification of the original proofs. We also describe the evolution of the WAY theorem from a strict no-go verdict for certain, highly idealized, precise measurements into a quantitative constraint on the accuracy and approximate repeatability of imprecise measurements.