Entropic distinguishability of quantum fields in phase space

Sara Ditsch; Tobias Haas

doi:10.22331/q-2024-07-17-1414

Entropic distinguishability of quantum fields in phase space

¹Physik Department, TUM School of Natural Sciences, Technische Universität München, James-Franck-Straße 1, 85748 Garching, Germany
²Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, Boltzmannstr. 8, 85748 Garching, Germany
³Centre for Quantum Information and Communication, École polytechnique de Bruxelles, CP 165, Université libre de Bruxelles, 1050 Brussels, Belgium

Published:	2024-07-17, volume 8, page 1414
Eprint:	arXiv:2307.06128v2
Doi:	https://doi.org/10.22331/q-2024-07-17-1414
Citation:	Quantum 8, 1414 (2024).

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Abstract

We present a general way of quantifying the entropic uncertainty of quantum field configurations in phase space in terms of entropic distinguishability with respect to the vacuum. Our approach is based on the functional Husimi $Q$-distribution and a suitably chosen relative entropy, which we show to be non-trivially bounded from above by the uncertainty principle. The resulting relative entropic uncertainty relation is as general as the concept of coherent states and thus holds for quantum fields of bosonic and fermionic type. Its simple form enables diverse applications, among which we present a complete characterization of the uncertainty surplus of arbitrary states in terms of the total particle number for a scalar field and the fermionic description of the Ising model. Moreover, we provide a quantitative interpretation of the role of the uncertainty principle for quantum phase transitions.

Featured image: Relative Entropic Uncertainty Relation (REUR) witnessing a Quantum Phase Transition (QPT).

► BibTeX data

@article{Ditsch2024entropic,
  doi = {10.22331/q-2024-07-17-1414},
  url = {https://doi.org/10.22331/q-2024-07-17-1414},
  title = {Entropic distinguishability of quantum fields in phase space},
  author = {Ditsch, Sara and Haas, Tobias},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1414},
  month = jul,
  year = {2024}
}

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arXiv:2404.12321

[110] Y. Deller, M. Gärttner, T. Haas, M. K. Oberthaler, M. Reh, and H. Strobel. ``Area laws for classical entropies in a spin-1 Bose-Einstein condensate'' (2024). arXiv:2404.12323.
arXiv:2404.12323

Cited by

[1] Markus Schröfl and Stefan Floerchinger, "Relative Entropy and Mutual Information in Gaussian Statistical Field Theory", Annales Henri Poincaré 26 9, 3233 (2025).

[2] Yannick Deller, Martin Gärttner, Tobias Haas, Markus K. Oberthaler, Moritz Reh, and Helmut Strobel, "Area laws and thermalization from classical entropies in a Bose-Einstein condensate", Physical Review A 112 1, L011303 (2025).

[3] Adrian M. Escobar Ruiz, Angelina N. Mendoza Tavera, Robin P. Sagar, C. Mateo Frausto-Avila, and Mario A. Quiroz-Juárez, "Wigner-entropy and negativity signatures of tunneling in a sextic double well", The European Physical Journal Plus 141 3, 240 (2026).

[4] Nicolas J. Cerf and Tobias Haas, "Information and Majorization Theory for Fermionic Phase-Space Distributions", Physical Review Letters 135 11, 110201 (2025).

[5] Markus Schröfl and Stefan Floerchinger, "Time evolution of relativistic quantum fields in spatial subregions", Physical Review D 111 2, 025009 (2025).

[6] Yannick Deller, Martin Gärttner, Tobias Haas, Markus K. Oberthaler, Moritz Reh, and Helmut Strobel, "Entropy estimation in a spin-1 Bose-Einstein condensate", New Journal of Physics 27 4, 043004 (2025).

[7] Tobias Haas, "Area laws from classical entropies", arXiv:2404.12320, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-12 21:22:40) and SAO/NASA ADS (last updated successfully 2026-08-12 21:22:41). The list may be incomplete as not all publishers provide suitable and complete citation data.

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