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QI: Fachverband Quanteninformation

QI 20: Concepts and Methods II

QI 20.2: Talk

Wednesday, March 8, 2023, 14:45–15:00, B302

Foundations of fermionic particle correlations — •Damiano Aliverti-Piuri, Kaustav Chatterjee, Lexin Ding, and Christian Schilling — LMU University, Faculty of Physics, Munich

Multipartite systems are an essential topic in Quantum information theory, and a comprehensive theory has been developed regarding the several kinds of correlations they can exhibit. Such correlations, especially entanglement, are both interesting on a theoretical level, and useful for quantum processing tasks. Our starting point is the well-established definitions of uncorrelated, classically correlated, and unentangled states of multipartite systems - for example, distinguishable particles. To these three sets of states correspond three correlation measures, based on geometric ideas: total correlation, quantum correlation, and relative entropy of entanglement. Inspired by recent work by other authors (Gigena and Rossignoli; Gottlieb and Mauser), we propose a systematic approach towards particle correlations in systems of indistinguishable particles, with an emphasis on fermions. We (i) give definitions of types of increasingly correlated fermionic states, and of the respective geometric correlation measures; (ii) motivate our definitions from the point of view of Resource theory; (iii) study some promising properties of these states and measures; (iv) obtain analytical formulas for 2-fermion systems and other simple cases.