Coarse-grained distinguishability of field interactions

Cédric Bény

Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
Department of Applied Mathematics, Hanyang University (ERICA), 55 Hanyangdaehak-ro, Ansan, Gyeonggi-do, 426-791, Korea

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Information-theoretical quantities such as statistical distinguishability typically result from optimisations over all conceivable observables. Physical theories, however, are not generally considered valid for all mathematically allowed measurements. For instance, quantum field theories are not meant to be correct or even consistent at arbitrarily small lengthscales. A general way of limiting such an optimisation to certain observables is to first coarse-grain the states by a quantum channel. We show how to calculate contractive quantum information metrics on coarse-grained equilibrium states of free bosonic systems (Gaussian states), in directions generated by arbitrary perturbations of the Hamiltonian. As an example, we study the Klein-Gordon field. If the phase-space resolution is coarse compared to h-bar, the various metrics become equal and the calculations simplify. In that context, we compute the scale dependence of the distinguishability of the quartic interaction.

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Cited by

[1] Cédric Bény, "Inferring relevant features: From QFT to PCA", International Journal of Quantum Information 16 08, 1840012 (2018).

[2] Vincent Lahoche, Dine Ousmane Samary, and Mohamed Tamaazousti, "Signal Detection in Nearly Continuous Spectra and ℤ2-Symmetry Breaking", Symmetry 14 3, 486 (2022).

[3] Amit Gordon, Aditya Banerjee, Maciej Koch-Janusz, and Zohar Ringel, "Relevance in the Renormalization Group and in Information Theory", Physical Review Letters 126 24, 240601 (2021).

[4] Vincent Lahoche, Mohamed Ouerfelli, Dine Ousmane Samary, and Mohamed Tamaazousti, "Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra II: Tensorial Data", Entropy 23 7, 795 (2021).

[5] Vincent Lahoche, Dine Ousmane Samary, and Mohamed Tamaazousti, "Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra I: Matricial Data", Entropy 23 9, 1132 (2021).

[6] H Erbin, V Lahoche, and D Ousmane Samary, "Non-perturbative renormalization for the neural network-QFT correspondence", Machine Learning: Science and Technology 3 1, 015027 (2022).

[7] Ludovico Lami, Siddhartha Das, and Mark M. Wilde, "Approximate reversal of quantum Gaussian dynamics", Journal of Physics A Mathematical General 51 12, 125301 (2018).

[8] Vincent Lahoche, Dine Ousmane Samary, and Mohamed Tamaazousti, "Signal detection in nearly continuous spectra and symmetry breaking", arXiv:2011.05447, (2020).

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The above citations are from Crossref's cited-by service (last updated successfully 2024-04-12 15:25:18) and SAO/NASA ADS (last updated successfully 2024-04-12 15:25:19). The list may be incomplete as not all publishers provide suitable and complete citation data.