A1 Refereed original research article in a scientific journal
Notes on Joint Measurability of Quantum Observables
Authors: Heinosaari T, Reitzner D, Stano P
Publisher: SPRINGER
Publication year: 2008
Journal:Foundations of Physics
Journal name in sourceFOUNDATIONS OF PHYSICS
Journal acronym: FOUND PHYS
Volume: 38
Issue: 12
First page : 1133
Last page: 1147
Number of pages: 15
ISSN: 0015-9018
DOI: https://doi.org/10.1007/s10701-008-9256-7
Abstract
For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly measurable, then their joint observable is unique and it gives the greatest lower bound for the effects corresponding to the observables; (iii) if we have two sharp observables and their every possible two outcome partitionings are jointly measurable, then the observables themselves are jointly measurable. We show that, in general, these properties do not hold. Also some possible candidates which would accompany joint measurability and generalize these apparently useful properties are discussed.
For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly measurable, then their joint observable is unique and it gives the greatest lower bound for the effects corresponding to the observables; (iii) if we have two sharp observables and their every possible two outcome partitionings are jointly measurable, then the observables themselves are jointly measurable. We show that, in general, these properties do not hold. Also some possible candidates which would accompany joint measurability and generalize these apparently useful properties are discussed.
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