Distinguishability measures and entropies for general probabilistic theories

Gen Kimura; Koji Nuida; Hideki Imai

doi:10.1016/S0034-4877(10)00025-X

Distinguishability measures and entropies for general probabilistic theories

Gen Kimura, Koji Nuida, Hideki Imai

Research output: Contribution to journal › Article › peer-review

37 Citations (Scopus)

Abstract

As a part of the construction of an information theory based on general probabilistic theories, we propose and investigate several distinguishability measures and "entropies" in general probabilistic theories. As their applications, no-cloning theorems, information-disturbance theorems are reformulated, and a bound of the accessible informations is discussed in general probabilistic theories, not resorting to quantum theory. We also propose the principle of equality for pure states which makes general probabilistic theories more realistic, and we discuss the role of entropies as a measure of pureness.

Original language	English
Pages (from-to)	175-206
Number of pages	32
Journal	Reports on Mathematical Physics
Volume	66
Issue number	2
DOIs	https://doi.org/10.1016/S0034-4877(10)00025-X
Publication status	Published - 2010 Oct
Externally published	Yes

Keywords

Distinguishability measures and entropies
Foundations of quantum theory
General probabilistic theories

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1016/S0034-4877(10)00025-X

Cite this

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AU - Kimura, Gen

AU - Nuida, Koji

AU - Imai, Hideki

N1 - Funding Information: We would like to thank for useful comments and discussions to Dr. Imafuku and Dr. Miyadera. This work was partially supported by Grant-in-Aid for Young Scientists (B) (No.20700017 and No.22740079), The Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

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N2 - As a part of the construction of an information theory based on general probabilistic theories, we propose and investigate several distinguishability measures and "entropies" in general probabilistic theories. As their applications, no-cloning theorems, information-disturbance theorems are reformulated, and a bound of the accessible informations is discussed in general probabilistic theories, not resorting to quantum theory. We also propose the principle of equality for pure states which makes general probabilistic theories more realistic, and we discuss the role of entropies as a measure of pureness.

AB - As a part of the construction of an information theory based on general probabilistic theories, we propose and investigate several distinguishability measures and "entropies" in general probabilistic theories. As their applications, no-cloning theorems, information-disturbance theorems are reformulated, and a bound of the accessible informations is discussed in general probabilistic theories, not resorting to quantum theory. We also propose the principle of equality for pure states which makes general probabilistic theories more realistic, and we discuss the role of entropies as a measure of pureness.

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Distinguishability measures and entropies for general probabilistic theories

Abstract

Keywords

ASJC Scopus subject areas

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