SAMOP 2023 – scientific programme

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QI: Fachverband Quanteninformation

QI 34: Concepts and Methods III

QI 34.2: Talk

Friday, March 10, 2023, 11:15–11:30, B302

Solution of the convex single-body quantum marginal problem and its physical relevance — •Julia Liebert¹, Federico Castillo², Jean-Philippe Labbé³, Arnau Padrol⁴, Eva Philippe⁴, Rolando Reiner¹, and Christian Schilling¹ — ¹University of Munich (LMU), Munich, Germany — ²Pontificia Universidad Catolica de Chile, Macul, Chile — ³École de Technologie Supérieure, Montréal, Canada — ⁴Sorbonne Université, Paris, France

The single-body quantum marginal problem asks whether given single-body reduced density matrices are compatible to some multipartite quantum state. In a recent breakthrough, A. Klyachko has solved this general problem on an abstract mathematical level. Urged by the limited scope of that solution to artificially small quantum systems, we explain why the convex-relaxed variant of that compatibility problem is the more relevant one for practical purposes. By using tools from convex analysis, we then provide a comprehensive solution to the latter problem for any multipartite quantum state with a fixed spectrum, leading to a complete hierarchy of necessary and sufficient spectral constraints which are valid for systems of arbitrary size. In the context of fermions and bosons, these novel conditions lead to a physical relevant generalization of Pauli’s famous exclusion principle.