No-free-information principle in general probabilistic theories
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 sho...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2019-07-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2019-07-08-157/pdf/ |
| _version_ | 1819195272210677760 |
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| author | Teiko Heinosaari Leevi Leppäjärvi Martin Plávala |
| author_facet | Teiko Heinosaari Leevi Leppäjärvi Martin Plávala |
| author_sort | Teiko Heinosaari |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-23T02:10:07Z |
| format | Article |
| id | doaj.art-75e2e7f76c8a4691a45dd2d9165f42d8 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-23T02:10:07Z |
| publishDate | 2019-07-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-75e2e7f76c8a4691a45dd2d9165f42d82022-12-21T18:03:48ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2019-07-01315710.22331/q-2019-07-08-15710.22331/q-2019-07-08-157No-free-information principle in general probabilistic theoriesTeiko HeinosaariLeevi LeppäjärviMartin PlávalaIn 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.https://quantum-journal.org/papers/q-2019-07-08-157/pdf/ |
| spellingShingle | Teiko Heinosaari Leevi Leppäjärvi Martin Plávala No-free-information principle in general probabilistic theories Quantum |
| title | No-free-information principle in general probabilistic theories |
| title_full | No-free-information principle in general probabilistic theories |
| title_fullStr | No-free-information principle in general probabilistic theories |
| title_full_unstemmed | No-free-information principle in general probabilistic theories |
| title_short | No-free-information principle in general probabilistic theories |
| title_sort | no free information principle in general probabilistic theories |
| url | https://quantum-journal.org/papers/q-2019-07-08-157/pdf/ |
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