Summary
The foundation of today’s information-oriented society is based on Information Theory. Entropy is a fundamental concept in both classical and quantum information theory, measuring the uncertainty and the information content present in the state of a physical system. The Asymptotic Equipartition Property (AEP) asserts that the entropy of smaller parts accumulates to produce the total entropy of the entire system, under the assumption that the individual parts are identical and independent. A remarkable generalization of this property is the Entropy Accumulation Theorem (EAT) which states that entropy accumulation occurs more generally without an independence assumption, provided one quantifies the uncertainty about the individual systems by the von Neumann entropy of suitably chosen conditional states. These two results are central in the asymptotic analysis of entropy measures in finite-dimensional quantum systems with a wide range of applications in data compression, source coding, and Quantum Key Distribution.
Despite major advances in the study of entropy in quantum information theory, the fundamental limitations of extending the above concepts to infinite-dimensional systems are far from being understood. The main objective of this project is to develop novel mathematical tools to overcome these difficulties and extend these ideas in the framework of abstract von Neumann algebras. In particular, our essential goal will be to establish two main concepts- Asymptotic Equipartition and Entropy Accumulation in von Neumann algebras acting on infinite-dimensional Hilbert spaces. As a consequence, the generalized version of these two concepts will have direct applications in continuous variable Quantum Key Distribution and other cryptographic protocols, representing a small but important contribution to the European Commission’s Quantum Technologies Flagship supporting pioneering research on quantum science.
Despite major advances in the study of entropy in quantum information theory, the fundamental limitations of extending the above concepts to infinite-dimensional systems are far from being understood. The main objective of this project is to develop novel mathematical tools to overcome these difficulties and extend these ideas in the framework of abstract von Neumann algebras. In particular, our essential goal will be to establish two main concepts- Asymptotic Equipartition and Entropy Accumulation in von Neumann algebras acting on infinite-dimensional Hilbert spaces. As a consequence, the generalized version of these two concepts will have direct applications in continuous variable Quantum Key Distribution and other cryptographic protocols, representing a small but important contribution to the European Commission’s Quantum Technologies Flagship supporting pioneering research on quantum science.
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| Web resources: | https://cordis.europa.eu/project/id/101108117 |
| Start date: | 01-08-2023 |
| End date: | 31-07-2025 |
| Total budget - Public funding: | - 211 754,00 Euro |
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Original description
The foundation of today’s information-oriented society is based on Information Theory. Entropy is a fundamental concept in both classical and quantum information theory, measuring the uncertainty and the information content present in the state of a physical system. The Asymptotic Equipartition Property (AEP) asserts that the entropy of smaller parts accumulates to produce the total entropy of the entire system, under the assumption that the individual parts are identical and independent. A remarkable generalization of this property is the Entropy Accumulation Theorem (EAT) which states that entropy accumulation occurs more generally without an independence assumption, provided one quantifies the uncertainty about the individual systems by the von Neumann entropy of suitably chosen conditional states. These two results are central in the asymptotic analysis of entropy measures in finite-dimensional quantum systems with a wide range of applications in data compression, source coding, and Quantum Key Distribution.Despite major advances in the study of entropy in quantum information theory, the fundamental limitations of extending the above concepts to infinite-dimensional systems are far from being understood. The main objective of this project is to develop novel mathematical tools to overcome these difficulties and extend these ideas in the framework of abstract von Neumann algebras. In particular, our essential goal will be to establish two main concepts- Asymptotic Equipartition and Entropy Accumulation in von Neumann algebras acting on infinite-dimensional Hilbert spaces. As a consequence, the generalized version of these two concepts will have direct applications in continuous variable Quantum Key Distribution and other cryptographic protocols, representing a small but important contribution to the European Commission’s Quantum Technologies Flagship supporting pioneering research on quantum science.
Status
SIGNEDCall topic
HORIZON-MSCA-2022-PF-01-01Update Date
31-07-2023
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