Generalized probabilistic theories and conic extensions of polytopes

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10318082" target="_blank" >RIV/00216208:11320/15:10318082 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1088/1751-8113/48/2/025302" target="_blank" >http://dx.doi.org/10.1088/1751-8113/48/2/025302</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8113/48/2/025302" target="_blank" >10.1088/1751-8113/48/2/025302</a>

Result language

angličtina

Original language name

Generalized probabilistic theories and conic extensions of polytopes

Original language description

Generalized probabilistic theories (GPT) provide a general framework that includes classical and quantum theories. It is described by a cone C and its dual C*. We show that whether some one-way communication complexity problems can be solved within a GPTis equivalent to the recently introduced cone factorization of the corresponding communication matrix M. We also prove an analogue of Holevo's theorem: when the cone C is contained in R-n, the classical capacity of the channel realized by sending GPT states and measuring them is bounded by log n. Polytopes and optimising functions over polytopes arise in many areas of discrete mathematics. A conic extension of a polytope is the intersection of a cone C with an affine subspace whose projection onto theoriginal space yields the desired polytope. Extensions of polytopes can sometimes be much simpler geometric objects than the polytope itself. The existence of a conic extension of a polytope is equivalent to that of a cone factorization o

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

IN - Informatics

OECD FORD branch

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Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2015

Confidentiality

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

Name of the periodical

Journal of Physics A: Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

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Volume of the periodical

48

Issue of the periodical within the volume

2

Country of publishing house

GB - UNITED KINGDOM

Number of pages

22

Pages from-to

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UT code for WoS article

000346414600010

EID of the result in the Scopus database

2-s2.0-84918503236