EPJ D - 'Measurement of Quantum Mechanical Operators' Revisited

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Published on 31 March 2011

Quantum mechanical measurements are often assumed to be accurate and repeatable. However, due to a fundamental result of Wigner (1952) and Araki and Yanase (1961), we now know that there are limitations to these properties in the presence of aconserved quantity that does not commute with the observable to be measured. Despite its importance and impact on quantum technologies, the full scope of this so-called WAY theorem has remained unclear.

In this recent paper in EPJ D, authors Loveridge and Busch combine case studies and extensions of existing theorems to provide a synthesis which sheds new light on the significance of the repeatability requirement. Their analysis highlights yet another condition that has remained largely underestimated: the requirement that the apparatus pointer observable commutes with the conserved quantity. They show that this condition alone entails that good measurement accuracy and repeatability can only be achieved if the apparatus has a large spread in the conserved quantity. The necessity of this size constraint is established for the first time in a model-independent way. Conversely, it is shown that there is no such size requirement for realizing arbitrarily accurate and repeatable, momentum-conserving measurements of position if one chooses a pointer that does not commute with momentum. With this result a long-standing open question posed by Stein and Shimony has thus been answered affirmatively.