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An information-theoretic account of the Wigner-Araki-Yanase theorem
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The Wigner-Araki-Yanase (WAY) theorem can be understood as a result in the resource theory of asymmetry asserting the impossibility of perfectly simulating, via symmetric processing, the measurement of an asymmetric observable unless one has access to a state that is perfectly asymmetric, that is, one whose orbit under the group action is a set of orthogonal states. The simulation problem can be characterized information-theoretically by considering how well both the target observable and the resource state can provide an encoding of an element of the symmetry group. Leveraging this information-theoretic perspective, we show that the WAY theorem is a consequence of the no-programming theorem for projective measurements. The connection allows us to clarify the conceptual content of the theorem and to deduce some interesting generalizations.
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Cited by 3 Pith papers
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Extends the Wigner-Araki-Yanase theorem to energy conservation by deriving error bounds and gate conditions for scattering-type quantum measurements and controlled operations.
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