Generalized Uncertainty and the WAY Theorem: Intrinsic and Operational Limits on Position Measurement

The uncertainty relation between the noise operator and the conserved quantity leads to a bound on the accuracy of general measurements. The bound extends the assertion by Wigner, Araki, and Yanase that conservation laws limit the accuracy of "repeatable," or "nondisturbing," measurements to general measurements, and improves the one previously obtained by Yanase for spin measurements. The bound represents an obstacle to making a small quantum computer.

arXiv:quant-ph/0112154Physical Review LettersJan 23, 200268 citations

Generalized Uncertainty and the WAY Theorem: Intrinsic and Operational Limits on Position Measurement

S. Zarrinkamar

Published Oct 30, 2026• 0 citations

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Abstract

DOI: 10.1364/opticaopen.34790334.v1

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L_{S}

is bounded, given a conserved total additive system plus apparatus quantity

L_{SA}

, the measurement operator

E_{S}

must commute with

L_{S}

. Prior proofs have exploited the properties of unitary evolution constrained by momentum conserving operations that tend to obscure the physical nature of the WAY theorem and as well lead to bounds on performance. As it is generally agreed that momentum is always exactly conserved in measurement, we instead develop a general angular momentum conserving model of measurement. This model is shown to lead to a simple explanation of the major implications of the WAY theorem and provides exact results of the effects of measurement based on the apparatus model. This is shown by both tracing the apparatus from the density matrix and also via a system-only channel model based on Kraus operators.