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This research advances quantum information theory by deriving closed-form expressions for the relative entropy of multi-mode squeezed states in relativistic quantum field theory. The study distinguishes between physically viable local-in-spacetime squeezing, which yields finite energy and entropy, and local-in-space configurations that result in divergent quantities. These findings clarify the mathematical boundaries of state distinguishability for continuum modes in Minkowski spacetime.
Finite relative entropy for locally squeezed states
arXiv:2511.11203v3 Announce Type: replace Abstract: Relative entropy serves as a fundamental measure of state distinguishability in both quantum information theory and relativistic quantum field theory. Despite its conceptual importance, however, explicit computations of relative entropy remain notoriously difficult. Thus far, results in closed form have only been obtained for ground states, coherent states, and, more recently, single-mode squeezed states. In this work, we extend the analysis to multi-mode squeezed states, imposing that the squeezing generators be local either in space or in spacetime, which results in a continuum of squeezed modes. We provide a detailed and self-contained analysis of such states for a free scalar quantum field on Minkowski spacetime, connecting also with older results on the essential self-adjointness of the Wick square, and showing that they lie in the folium of the Minkowski vacuum representation. We uncover that local-in-space squeezing leads to physically unreasonable states which have a divergent energy density and relative entropy, while local-in-spacetime squeezing provides a physically reasonable class of states with finite relative entropy.
Abstract:Relative entropy serves as a fundamental measure of state distinguishability in both quantum information theory and relativistic quantum field theory. Despite its conceptual importance, however, explicit computations of relative entropy remain notoriously difficult. Thus far, results in closed form have only been obtained for ground states, coherent states, and, more recently, single-mode squeezed states. In this work, we extend the analysis to multi-mode squeezed states, imposing that the squeezing generators be local either in space or in spacetime, which results in a continuum of squeezed modes. We provide a detailed and self-contained analysis of such states for a free scalar quantum field on Minkowski spacetime, connecting also with older results on the essential self-adjointness of the Wick square, and showing that they lie in the folium of the Minkowski vacuum representation. We uncover that local-in-space squeezing leads to physically unreasonable states which have a divergent energy density and relative entropy, while local-in-spacetime squeezing provides a physically reasonable class of states with finite relative entropy.
36 pages; new results on local squeezing in spacetime (Section 4.3, Appendix D), minor changes throughout the rest
arXiv:2511.11203 [quant-ph]
(or arXiv:2511.11203v3 [quant-ph] for this version)
From: Jan M. Mandrysch [view email] [v1] Fri, 14 Nov 2025 12:02:10 UTC (46 KB) [v2] Fri, 28 Nov 2025 10:10:39 UTC (47 KB) [v3] Wed, 16 Sep 2026 17:21:58 UTC (43 KB)
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