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Generalized Conditional Entropies of Partitions on Quantum Logic

Alexey, Rastegin

For partitions on quantum logic, the Renyi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.

理论物理通讯：英文版Jan 1, 20120 citations

Generalized Conditional Entropies of Partitions on Quantum Logic

Alexey E. Rastegin

For partitions on quantum logic, the Rényi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.

Communications in Theoretical PhysicsDec 1, 20127 citations

Conditional R-norm entropy and R-norm divergence in quantum logics

Mohammad Hossein Zarenezhad, Abolfazl Ebrahimzadeh

‎This contribution ‎‎deals with the mathematical modeling of R-norm entropy and R-norm divergence in quantum logics. ‎‎W‎e extend some results concerning the R-norm entropy and conditional R-norm entropy given in (Inf. Control 45, 1980), ‎‎‎‎‎to ‎the‎ quantum logics.‎ Firstly, the concepts of ‎‎R-norm entropy ‎and‎ ‎conditional R-norm entropy in quantum logics are introduced. ‎We ‎prove‎ ‎the concavity property for the notion of R-norm entropy in quantum logics ‎and we ‎show‎‎ that this entropy measure does not have the property of sub-additivity in a true sense. ‎It ‎is ‎prove‎n that ‎‎‎the monotonicity ‎property ‎for ‎the suggested type of ‎conditional ‎version ‎of ‎R-norm ‎entropy, holds. Furthermore, we introduce the concept of R-norm divergence of states in quantum logics and we derive basic properties of this quantity. ‎In particular‎, a relationship between the R-norm divergence and the R-norm entropy of partitions is provided.‎‎‎‎This contribution ‎‎deals with the mathematical modeling of R-norm entropy and R-norm divergence in quantum logics. ‎‎W‎e extend some results concerning the R-norm entropy and conditional R-norm entropy given in (Inf. Control 45, 1980), ‎‎‎‎‎to ‎the‎ quantum logics.‎ Firstly, the concepts of ‎‎R-norm entropy ‎and‎ ‎conditional R-norm entropy in quantum logics are introduced. ‎We ‎prove‎ ‎the concavity property for the notion of R-norm entropy in quantum logics ‎and we ‎show‎‎ that this entropy measure does not have the property of sub-additivity in a true sense. ‎It ‎is ‎prove‎n that ‎‎‎the monotonicity ‎property ‎for ‎the suggested type of ‎conditional ‎version ‎of ‎R-norm ‎entropy, holds. Furthermore, we introduce the concept of R-norm divergence of states in quantum logics and we derive basic properties of this quantity. ‎In particular‎, a relationship between the R-norm divergence and the R-norm entropy of partitions is provided.‎‎‎

Journal of mathematical extension.Jul 22, 20200 citations

Logical entropy of quantum dynamical systems

Abolfazl Ebrahimzadeh

Abstract This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.

Open PhysicsJan 1, 201616 citations

Entropy of Partitions on Sequential Effect Algebras

Wang Jia-Mei, Junde Wu, Cho Minhyung

By using the sequential effect algebra theory, we establish the partitions and refinements of quantum logics and study their entropies.

Communications in Theoretical PhysicsMar 1, 20106 citations

Entropy of Partitions on Sequential Effect Algebras

Jiamei, Wang, Junde, Wu, Minhyung, Cho

By using the sequential effect algebra theory, we establish the partitions and refinements of quantum logics and study their entropies.

arXiv:0908.2510Aug 18, 20090 citations

Conditional Entropy of Partitions on Quantum Logic

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Conditional Entropy of Partitions on Quantum Logic

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