The WAY theorem and the quantum resource theory of asymmetry

Abstract

The WAY theorem establishes an important constraint that conservation laws impose on quantum mechanical measurements. We formulate the WAY theorem in the broader context of resource theories, where one is constrained to a subset of quantum mechanical operations described by a symmetry group. Establishing connections with the theory of quantum state discrimination we obtain optimal unitaries describing the measurement of arbitrary observables, explain how prior information can permit perfect measurements that circumvent the WAY constraint, and provide a framework that establishes a natural ordering on measurement apparatuses through a decomposition into asymmetry and charge subsystems.

11 pages, 3 figures

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• Factorization, coherence and asymmetry in the Heisenberg spin-1/2 XXZ chain a transverse magnetic field and with Dzyaloshinskii-Moriya interaction
• Units of rotational information
• Optimal asymptotic cloning machines
• Entanglement-assisted communication in the absence of shared reference frame
• WAY beyond conservation laws
• Quantum energetics of a non-commuting measurement