Unique Information Through the Lens of Channel Ordering: An Introduction and Review
The problem of constructing information measures with a well-defined interpretation is of fundamental significance in information theory. A good definition of an information measure entails certain desirable properties while also providing answers to operational problems. In this work, we investigat...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/1/29 |
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| author | Pradeep Kr. Banerjee |
| author_facet | Pradeep Kr. Banerjee |
| author_sort | Pradeep Kr. Banerjee |
| collection | DOAJ |
| description | The problem of constructing information measures with a well-defined interpretation is of fundamental significance in information theory. A good definition of an information measure entails certain desirable properties while also providing answers to operational problems. In this work, we investigate the properties of the unique information, an information measure that quantifies a deviation from the Blackwell order. Beyond providing an accessible introduction to the topic from a channel ordering perspective, we present a novel resource-theoretic characterization of unique information in a cryptographic task related to secret key agreement. Our operational view of unique information entails rich physical intuition that leads to new insights into secret key agreement in the context of non-negative decompositions of the mutual information into redundant and synergistic contributions. Through this lens, we illuminate new directions for research in partial information decompositions and information-theoretic cryptography. |
| format | Article |
| id | doaj-art-a7d6c82095884d6bb5a4cbc1ea6b72a3 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-a7d6c82095884d6bb5a4cbc1ea6b72a32025-01-24T13:31:43ZengMDPI AGEntropy1099-43002025-01-012712910.3390/e27010029Unique Information Through the Lens of Channel Ordering: An Introduction and ReviewPradeep Kr. Banerjee0Institute for Data Science Foundations, Blohmstraße 15, 21079 Hamburg, GermanyThe problem of constructing information measures with a well-defined interpretation is of fundamental significance in information theory. A good definition of an information measure entails certain desirable properties while also providing answers to operational problems. In this work, we investigate the properties of the unique information, an information measure that quantifies a deviation from the Blackwell order. Beyond providing an accessible introduction to the topic from a channel ordering perspective, we present a novel resource-theoretic characterization of unique information in a cryptographic task related to secret key agreement. Our operational view of unique information entails rich physical intuition that leads to new insights into secret key agreement in the context of non-negative decompositions of the mutual information into redundant and synergistic contributions. Through this lens, we illuminate new directions for research in partial information decompositions and information-theoretic cryptography.https://www.mdpi.com/1099-4300/27/1/29comparison of channelsunique informationBlackwell orderinformation-theoretic cryptographysecret key ratesecrecy monotones |
| spellingShingle | Pradeep Kr. Banerjee Unique Information Through the Lens of Channel Ordering: An Introduction and Review Entropy comparison of channels unique information Blackwell order information-theoretic cryptography secret key rate secrecy monotones |
| title | Unique Information Through the Lens of Channel Ordering: An Introduction and Review |
| title_full | Unique Information Through the Lens of Channel Ordering: An Introduction and Review |
| title_fullStr | Unique Information Through the Lens of Channel Ordering: An Introduction and Review |
| title_full_unstemmed | Unique Information Through the Lens of Channel Ordering: An Introduction and Review |
| title_short | Unique Information Through the Lens of Channel Ordering: An Introduction and Review |
| title_sort | unique information through the lens of channel ordering an introduction and review |
| topic | comparison of channels unique information Blackwell order information-theoretic cryptography secret key rate secrecy monotones |
| url | https://www.mdpi.com/1099-4300/27/1/29 |
| work_keys_str_mv | AT pradeepkrbanerjee uniqueinformationthroughthelensofchannelorderinganintroductionandreview |