Lüders Theorem for Unsharp Quantum Measurements
arXiv:1304.0054 · doi:10.1016/S0375-9601(98)00704-X
Abstract
A theorem of Lüders states that an ideal measurement of a sharp discrete observable does not alter the statistics of another sharp observable if, and only if, the two observables commute. It will be shown that this statement extends to certain pairs of unsharp observables. Implications for local relativistic quantum theory will be discussed.
Cited by in corpus (26)
- Characterizing quantum theory in terms of information-theoretic constraints
- A Unified and Generalized Approach to Quantum Error Correction
- Information Tradeoff Relations for Finite-Strength Quantum Measurements
- Non-disturbing quantum measurements
- Toy Model for a Relational Formulation of Quantum Theory
- Commutativity up to a factor of bounded operators in complex Hilbert space
- Unsharp Localization and Causality in Relativistic Quantum Theory
- Uniqueness and order in sequential effect algebras
- Simultaneous Measurement of Two Quantum Observables: Compatibility, Broadcasting, and In-between
- Fixed points of commutative Lüders operations
- Inequalities that test locality in quantum mechanics
- On Fixed Points of Lüders Operation
- Quotient-Comprehension Chains
- Quantum measurements constrained by the third law of thermodynamics
- Robust certification of arbitrary outcome quantum measurements from temporal correlations
- Universal collective rotation channels and quantum error correction
- Measures of disturbance and incompatibility for quantum measurements
- Measurement disturbance and conservation laws in quantum mechanics
- A disturbance tradeoff principle for quantum measurements
- Quantum incompatibility from the viewpoint of entanglement theory
- Lueders Theorem for Coherent-State POVMs
- Beyond the Projection Postulate and Back: Quantum Theories with Generalised State-Update Rules
- Connecting Commutativity and Classicality for Multi-Time Quantum Processes
- Shared randomness allows violation of macroscopic realism using a single measurement
- Decoherence free algebra
- Information storage and transmission under Markovian noise