Descrizione del progetto
Porre una solida base matematica per l’entropia quantistica
Nel regno quantistico, l’entropia è fondamentale per quantificare la quantità di informazioni e correlazioni presenti nei sistemi quantistici. A differenza dei sistemi descritti dalla meccanica classica, la conoscenza matematica dell’entropia per i sistemi quantistici è molto più limitata. Il progetto QEntropy, finanziato dall’UE, si propone di aumentare la comprensione della matematica dell’entropia quantistica. In particolare, il progetto svilupperà nuovi metodi matematici nell’analisi matriciale e nella teoria dell’ottimizzazione che creeranno le basi per un framework computazionale di algoritmi di approssimazione. Si prevede che il nuovo framework risolva una moltitudine di problemi fondamentali nella scienza dell’informazione quantistica.
Obiettivo
Entropy for quantum systems is the fundamental, interdisciplinary concept to quantify the advantage of quantum technologies for processing of information. It is well-established that the quantum advantage originates from the strong correlations found in the entanglement spectrum of multipartite quantum states, as exactly characterised by the information-theoretic tool quantum entropy. Contrary to the case of classical systems, however, our knowledge about the mathematics of quantum entropy is much more limited. Nonetheless, special entropy inequalities that are known to hold in the quantum case, such as the strong sub-additivity of quantum entropy, give crucial insights into the entanglement structure of multipartite quantum states. In this project, I will focus on understanding multipartite entropic constraints, which will lead to tight characterisations of the ultimate, physical limits of quantum information processing.
My recent mathematical works in quantum information led to operational extensions of the concept of strong sub-additivity from the seventies. Starting from that, I propose a research program that will lead to an understanding of quantum entropy that is on the same level as for the classical, commutative case. In the first part of my project, I will establish techniques in matrix analysis and optimisation theory to understand the interplay of arbitrarily many non-commuting operators. This mathematical framework will allow to prove novel quantum entropy inequalities that lead to refined approximations on the entanglement structure of multipartite quantum states. Second, I will employ the newly obtained entropic constraints to derive approximation algorithms for a plethora of fundamental problems in quantum information science. This includes schemes for achieving the physical limits of cryptography, resolving entropic additivity questions in information theory, and providing algorithms for the description of strongly interacting many body systems.
Campo scientifico
- natural sciencesphysical sciencesquantum physics
- natural sciencescomputer and information sciencescomputer securitycryptography
- engineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringcomputer hardwarequantum computers
- natural sciencesmathematics
Programma(i)
Argomento(i)
Meccanismo di finanziamento
ERC-STG - Starting GrantIstituzione ospitante
52062 Aachen
Germania