Project description DEENESFRITPL Laying a strong mathematical basis for quantum entropy In the quantum realm, entropy is fundamental to quantifying the amount of information and correlations that are present in quantum systems. Unlike for systems described by classical mechanics, the mathematical knowledge of entropy for quantum systems is much more limited. The EU-funded QEntropy project aims to increase understanding of the mathematics of quantum entropy. In particular, the project will develop novel mathematical methods in matrix analysis and optimisation theory that will build the basis for a computational framework of approximation algorithms. The new framework is expected to solve a plethora of fundamental problems in quantum information science. Show the project objective Hide the project objective Objective 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. Fields of science natural sciencesphysical sciencesquantum physicsnatural sciencescomputer and information sciencescomputer securitycryptographyengineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringcomputer hardwarequantum computersnatural sciencesmathematics Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2020-STG - ERC STARTING GRANTS Call for proposal ERC-2020-STG See other projects for this call Funding Scheme ERC-STG - Starting Grant Coordinator RHEINISCH-WESTFAELISCHE TECHNISCHE HOCHSCHULE AACHEN Net EU contribution € 1 499 835,00 Address Templergraben 55 52062 Aachen Germany See on map Region Nordrhein-Westfalen Köln Städteregion Aachen Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 Beneficiaries (2) Sort alphabetically Sort by Net EU contribution Expand all Collapse all RHEINISCH-WESTFAELISCHE TECHNISCHE HOCHSCHULE AACHEN Germany Net EU contribution € 1 499 835,00 Address Templergraben 55 52062 Aachen See on map Region Nordrhein-Westfalen Köln Städteregion Aachen Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE Participation ended United Kingdom Net EU contribution € 0,00 Address South kensington campus exhibition road SW7 2AZ London See on map Region London Inner London — West Westminster Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
