Post-processing minimal joint observables
arXiv:1808.10222 · doi:10.1088/1751-8121/aaf7bb
Abstract
A finite set of quantum observables (positive operator valued measures) is called compatible if these observables are marginals of a some observable, called a joint observable of them. For a given set of compatible observables, their joint observable is in general not unique and it is desirable to take a minimal joint observable in the post-processing order since a less informative observable disturbs less the system. We address the question of the minimality of finite-outcome joint observables and prove that any joint observable is lower bounded by a minimal joint observable in the post-processing order. We also give characterizations of the minimality of a joint observable that can be checked by finite-step algorithms and apply them to the case of non-commuting dichotomic qubit observables.
References in corpus (11)
- An Invitation to Quantum Incompatibility
- Clean Positive Operator Valued Measures
- Notes on Joint Measurability of Quantum Observables
- Commutative POVMs and Fuzzy Observables
- Coexistence of qubit effects
- Coexistence of qubit effects
- Optimal measurements in quantum mechanics
- Qualitative Noise-Disturbance Relation for Quantum Measurements
- When do pieces determine the whole? Extremal marginals of a completely positive map
- Minimal sufficient positive-operator valued measure on a separable Hilbert space
- Uniqueness of the joint measurement and the structure of the set of compatible quantum measurements