Quantum Measurements Generating Structures of Numerical Events

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73587183" target="_blank" >RIV/61989592:15310/18:73587183 - isvavai.cz</a>

Result on the web

<a href="https://file.scirp.org/pdf/JAMP_2018052114332952.pdf" target="_blank" >https://file.scirp.org/pdf/JAMP_2018052114332952.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4236/jamp.2018.65085" target="_blank" >10.4236/jamp.2018.65085</a>

Result language

angličtina

Original language name

Quantum Measurements Generating Structures of Numerical Events

Original language description

Let S be a set of states of a physical system and the probability of an occurrence of an event when the system is in state . The function p from S to is called a numerical event, multidimensional probability or, more precisely, S-probability. If a set of numerical events is ordered by the order of real functions one obtains a partial ordered set P in which the sum and difference of S-probabilities are related to their order within P. According to the structure that arises, this further opens up the opportunity to decide whether one deals with a quantum mechanical situation or a classical one. In this paper we focus on the situation that P is generated by a given set of measurements, i.e. S-probabilities, without assuming that these S-probabilities can be complemented by further measurements or are embeddable into Boolean algebras, assumptions that were made in most of the preceding papers. In particular, we study the generation by S-probabilities that can only assume the values 0 and 1, thus dealing with so called concrete logics. We characterize these logics under several suppositions that might occur with measurements and generalize our findings to arbitrary S-probabilities, this way providing a possibility to distinguish between potential classical and quantum situations and the fact that an obtained structure might not be sufficient for an appropriate decision. Moreover, we provide some explanatory examples from physics.

Czech name

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Czech description

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Type

J_ost - Miscellaneous article in a specialist periodical

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Applied Mathematics and Physics

ISSN

2327-4352

e-ISSN

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Volume of the periodical

6

Issue of the periodical within the volume

5

Country of publishing house

US - UNITED STATES

Number of pages

15

Pages from-to

982-996

UT code for WoS article

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EID of the result in the Scopus database

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