Generalized probabilistic theories and conic extensions of polytopes

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Generalized probabilistic theories and conic extensions of polytopes

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Generalized probabilistic theories and conic extensions of polytopes

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Journal of Physics A: Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

—

Svazek periodika

48

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

22

Strana od-do

—

Kód UT WoS článku

000346414600010

EID výsledku v databázi Scopus

2-s2.0-84918503236