WAY beyond conservation laws
arXiv:1611.05905 · doi:10.1103/PhysRevA.95.012127
Abstract
The ability to measure every quantum observable is ensured by a fundamental result in quantum measurement theory. Nevertheless, additive conservation laws associated with physical symmetries, such as the angular momentum conservation, may lead to restrictions on the measurability of the observables. Such limitations are imposed by the theorem of Wigner, Araki and Yanase (WAY). In this paper a new formulation of the WAY-theorem is presented rephrasing the measurability limitations in terms of quantum incompatibility. This broader mathematical basis enables us to both capture and generalise the WAY-theorem by allowing to drop the assumptions of additivity and even conservation of the involved quantities. Moreover, we extend the WAY-theorem to the general level of positive operator valued measures.
8 pages (double column), 2 figures
References in corpus (17)
- An Invitation to Quantum Incompatibility
- The WAY theorem and the quantum resource theory of asymmetry
- Conservative Quantum Computing
- Conservation laws, uncertainty relations, and quantum limits of measurements
- The Standard Model of Quantum Measurement Theory: History and Applications
- How energy conservation limits our measurements
- Efficient universal programmable quantum measurements
- 'Measurement of Quantum Mechanical Operators' Revisited
- Position Measurements Obeying Momentum Conservation
- Strongly Incompatible Quantum Devices
- Gate fidelity of arbitrary single-qubit gates constrained by conservation laws
- Completely positive maps on modules, instruments, extremality problems, and applications to physics
- Conservation-Law-Induced Quantum Limits for Physical Realizations of the Quantum NOT Gate
- When do pieces determine the whole? Extremal marginals of a completely positive map
- Wigner-Araki-Yanase theorem on Distinguishability
- Quantum Limits of Measurements Induced by Multiplicative Conservation Laws: Extension of the Wigner-Araki-Yanase Theorem
- Notes on Deterministic Programming of Quantum Observables and Channels