Relative entropic uncertainty relation for scalar quantum fields

2021/07/31 by Stefan Floerchinger, Tobias Haas, T. Haas +1
Computer Science · Mathematics · Physics and Astronomy · #Entropic uncertainty #Entropy (arrow of time) #Generalization #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum field theory #Quantum mechanics #Scalar (mathematics) #Statistical physics #Theoretical physics #Uncertainty principle #hep-th #quant-ph

paper · pdf · doi:10.21468/scipostphys.12.3.089

published as SciPost Phys. 12, 089 (2022) · 11 pages, 1 figure, published version

openalex publication_date 2022/03/10 · arxiv created 2022/03/11 · arxiv updated 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Entropic uncertainty is a well-known concept to formulate uncertainty relations for continuous variable quantum systems with finitely many degrees of freedom. Typically, the bounds of such relations scale with the number of oscillator modes, preventing a straight-forward generalization to quantum field theories. In this work, we overcome this difficulty by introducing the notion of a functional relative entropy and show that it has a meaningful field theory limit. We present the first entropic uncertainty relation for a scalar quantum field theory and exemplify its behavior by considering few particle excitations and the thermal state. Also, we show that the relation implies the multidimensional Heisenberg uncertainty relation.

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