Position Measurements Obeying Momentum Conservation

TL;DR

This paper reveals a fundamental limitation in quantum position measurements imposed by momentum conservation, extending the WAY theorem, and highlights the necessity of large momentum uncertainty in the apparatus for accuracy.

Contribution

It extends the WAY theorem to include position measurements under momentum conservation, identifying a new fundamental limitation.

Findings

Accurate position measurements require large momentum uncertainty in the apparatus.

Position measurement accuracy is fundamentally limited by momentum conservation.

The result generalizes the WAY theorem to new measurement scenarios.

Abstract

We present a hitherto unknown fundamental limitation to a basic measurement: that of the position of a quantum object when the total momentum of the object and apparatus is conserved. This result extends the famous Wigner-Araki-Yanase (WAY) theorem, and shows that accurate position measurements are only practically feasible if there is a large momentum uncertainty in the apparatus.