HEИндивидуална стипендия2023–2025

PENNSION · Partition and accumulation of ENtropy in infinite-dimeNSIONs

„Хоризонт Европа“ — Действия „Мария Склодовска-Кюри“

Период: 2023-08-01 → 2025-07-31
Финансиране от ЕС: 211 755 €
Участници: 1
Схема: HORIZON-TMA-MSCA-PF-EF

Линиите свързват координатора с партньорите.

Накратко на български

Квантовата информационна теория тук се прилага върху системи с безкрайни измерения, като например при компресирането на данни. Това помага за създаването на по-точна математическа основа за бъдещи технологии в областта на комуникациите и криптографията.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Partition and accumulation of ENtropy in infinite-dimeNSIONs

Quantum information theory lies at the heart of the next technological revolution, offering transformative possibilities in computation, communication, and cryptography. As Europe advances its strategic agenda through initiatives like the Quantum Flagship, there is a growing need to establish a rigorous theoretical foundation for quantum technologies that not only captures the operational aspects but also aligns with the physical realities of quantum systems, many of which are inherently infinite-dimensional. This project addressed a key gap in the existing theoretical landscape: the lack of a comprehensive understanding of foundational theorems such as the Asymptotic Equipartition Property (AEP) and the Entropy Accumulation Theorem (EAT) in the general setting of von Neumann algebras, which provide the mathematical language for infinite-dimensional quantum systems. These theorems are central to quantum information processing tasks, including data compression, statistical inference, and security proofs in cryptography. The primary objective of the project was to extend these cornerstone results to the infinite-dimensional setting and thereby offer a rigorous and broadly applicable framework for quantum information theory beyond the limitations of finite-dimensional models. Achieving this required a deep synthesis of ideas from operator algebras, quantum physics, and information theory — reflecting a truly interdisciplinary effort that draws from both the physical sciences and mathematical foundations. The project also explored how these results apply under structural constraints, such as those arising from subalgebras, which naturally appear in many real-world scenarios involving symmetries, partial observations, or operational limitations. The anticipated impact of this work is both theoretical and strategic. By strengthening the mathematical infrastructure underpinning quantum technologies. It opens up new avenues for applying advanced mathematical tools to practical quantum protocols, including those used in secure communication and quantum cryptography. At scale, these results contribute to Europe's leadership in quantum science, helping ensure that the foundational understanding of quantum systems keeps pace with technological innovation.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

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.

Оригинален текст от CORDIS (на английски).

Участници

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE · Le Chesnay CedexКоординаторФранция