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Paper Abstract and Keywords
Presentation 2017-05-30 10:10
Total Detection Probability in Generalized Probability Theories -- channel capacity and geometry of the state space --
Keiji Matsumoto (STI), Gen Kimura (SIT)
Abstract (in Japanese) (See Japanese page) 
(in English) The qubit state space is a beautiful sphere, but the high-dimensional one is increasingly asymmetric in proportion to the dimension. Similar observations also apply to classical systems. Here, we investigate this phenomenon in the light of general probabilistic theory, and conclude “the asymmetry is caused by the increase of contained information.” To start, we introduce total detection probability $N$ of a set of states, and show it nicely quantifies asymmetry of the state space. Next, information theoretic meaning of $N$ is investigated. Almost by definition, $N$ is not less than the number of distinguishable states, and by application of $N$ to the set of the receiver's states of a channel, we obtain the (maximized) product of the number of messages and the success probability of decode. In quantum mechanical systems, $N$ is written using Renner's max-relative entropy, and an upper bound to the channel capacity by $N$ is compared with Holevo's bound.
Keyword (in Japanese) (See Japanese page) 
(in English) quantum information / general probablistic theory / channel capacity / Holevo's theorem / state discrimination / / /  
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Conference Information
Committee QIT  
Conference Date 2017-05-29 - 2017-05-30 
Place (in Japanese) (See Japanese page) 
Place (in English) Ritesumeikan University, Suzaku Campus 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Quantum Information 
Paper Information
Registration To QIT 
Conference Code 2017-05-QIT 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Total Detection Probability in Generalized Probability Theories 
Sub Title (in English) channel capacity and geometry of the state space 
Keyword(1) quantum information  
Keyword(2) general probablistic theory  
Keyword(3) channel capacity  
Keyword(4) Holevo's theorem  
Keyword(5) state discrimination  
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1st Author's Name Keiji Matsumoto  
1st Author's Affiliation National Institute of Informatics (STI)
2nd Author's Name Gen Kimura  
2nd Author's Affiliation Shibaura Institute of Technology (SIT)
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Speaker Author-1 
Date Time 2017-05-30 10:10:00 
Presentation Time 20 minutes 
Registration for QIT 
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