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APPLICATIONS OF FREE PROBABILITY TO QUANTUM INFORMATION THEORY (Mathematical Studies on Independence and Dependence Structure : Algebra meets Probability)

open access: yesAPPLICATIONS OF FREE PROBABILITY TO QUANTUM INFORMATION THEORY (Mathematical Studies on Independence and Dependence Structure : Algebra meets Probability)
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QUANTIZATION OF INFORMATION THEORY (Mathematical Studies on Independence and Dependence Structure : Algebra meets Probability)

open access: yesQUANTIZATION OF INFORMATION THEORY (Mathematical Studies on Independence and Dependence Structure : Algebra meets Probability)
openaire  

On Independence of Events in Noncommutative Probability Theory [PDF]

open access: closedLobachevskii Journal of Mathematics, 2021
Abstract: We consider a tracial state ϕ on a von Neumann algebra A and assume that projections P, Q of A are independent if ϕ(PQ) = ϕ(P)ϕ(Q). First we present the general criterion of a projection pair independence. We then give a geometric criterion for independence of different pairs of projections.
Bikchentaev A.M., Ivanshin P.N.
semanticscholar   +3 more sources

Qualitative independence in probability theory [PDF]

open access: closedTheory and Decision, 1978
Probability theory is measure theory specialized by assumptions having to do with stochastic independence. Delete from probability and statistics those theorems that explicitly or implicitly (e.g., by postulating a random sample) invoke independence, and relatively little remains.
R. Duncan Luce   +3 more
semanticscholar   +3 more sources

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