Berlin 2024 – scientific programme

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QI: Fachverband Quanteninformation

QI 29: Quantum Information: Concept and Methods II

QI 29.1: Talk

Thursday, March 21, 2024, 15:00–15:15, HFT-TA 441

Information and uncertainty in the fermionic phase space — Nicolas Cerf and •Tobias Haas — Centre for Quantum Information and Communication, Université libre de Bruxelles, Belgium

We put forward several information-theoretic measures for the information encoded in phase-space distributions of a single fermion using the theory of supernumbers. In contrast to the bosonic case, the anti-commuting nature of Grassmann variables allow us to provide simple expressions for the phase-space distributions of arbitrary physical states. We show that all physical states are Gaussian and thus can be described by positive (negative) thermal Wigner W-distributions of positive (negative) temperature. We prove uncertainty relations for general measures of disorder, including, e.g. the fermionic analogs of the unproven phase-space majorization and Wigner entropy conjectures as well as the Lieb-Solovej theorem and the Wehrl-Lieb inequality.

Keywords: Fermions; Entropic uncertainty relations; Majorization relations; Phase-space distributions; Supernumbers