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 / / / |
Reference Info. |
IEICE Tech. Rep. |
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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 |
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quantum information |
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general probablistic theory |
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channel capacity |
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Holevo's theorem |
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state discrimination |
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1st Author's Name |
Keiji Matsumoto |
1st Author's Affiliation |
National Institute of Informatics (STI) |
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Gen Kimura |
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Shibaura Institute of Technology (SIT) |
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Date Time |
2017-05-30 10:10:00 |
Presentation Time |
20 minutes |
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QIT |
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