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Quantum Measurements Constrained by Symmetry

Leon Loveridge, University of British Columbia

(Session 7a : Friday from 5:00 - 5:30)

Abstract. The Wigner-Araki-Yanase (WAY) theorem prescribes limitations to quantum measurements under the constraint of a particular symmetry: that of an additive conserved quantity on the Hilbert space of the system and measuring apparatus. Any observable not commuting with such a quantity does not admit accurate and repeatable measurements. For example, a WAY constraint is known to inhibit the implementability of qubit operations if angular momentum conservation is to be respected. Furthermore, it has been shown recently that the WAY theorem extends in many respects to position measurements obeying momentum conservation. They key to achieving measurements with high accuracy is to allow the measuring apparatus to become large, quantified by the spread of the conserved quantity in its initial state. I'll review these results with specific reference to WAY constraints in quantum information processing, highlighting the important roles of the repeatability of the measurement and another often neglected condition: that the observable representing a pointer also commutes with the conserved quantity (called the Yanase condition). With this in mind, I'll briefly discuss how WAY-type restrictions occur in the alternative framework of quantum reference frames, where similar behaviour is observed, and present some new results in this context.