A1 Refereed original research article in a scientific journal
No-free-information principle in general probabilistic theories
Authors: Heinosaari T, Leppäjärvi L, Plávala M
Publisher: VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF
Publication year: 2019
Journal: Quantum
Journal name in source: QUANTUM
Journal acronym: QUANTUM-AUSTRIA
Volume: 3
First page : 157
Number of pages: 39
ISSN: 2521-327X
eISSN: 2521-327X
DOI: https://doi.org/10.22331/q-2019-07-08-157
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/41854588
Abstract
In quantum theory, the no-information-without-disturbance and no-free-information theorems express that those observables that do not disturb the measurement of another observable and those that can be measured jointly with any other observable must be trivial, i.e., coin tossing observables. We show that in the framework of general probabilistic theories these statements do not hold in general and continue to completely specify these two classes of observables. In this way, we obtain characterizations of the probabilistic theories where these statements hold. As a particular class of state spaces we consider the polygon state spaces, in which we demonstrate our results and show that while the no-information-without-disturbance principle always holds, the validity of the no-free-information principle depends on the parity of the number of vertices of the polygons.
In quantum theory, the no-information-without-disturbance and no-free-information theorems express that those observables that do not disturb the measurement of another observable and those that can be measured jointly with any other observable must be trivial, i.e., coin tossing observables. We show that in the framework of general probabilistic theories these statements do not hold in general and continue to completely specify these two classes of observables. In this way, we obtain characterizations of the probabilistic theories where these statements hold. As a particular class of state spaces we consider the polygon state spaces, in which we demonstrate our results and show that while the no-information-without-disturbance principle always holds, the validity of the no-free-information principle depends on the parity of the number of vertices of the polygons.
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