Year: 2026
Type: preprint
Abstract: Positive Wigner functions can have less Shannon entropy than the vacuum, even arbitrarily close to the vacuum state. We construct physical counterexamples and identify the competition that controls their entropy: the relative entropy to the vacuum phase-space density can exceed twice the mean photon number. A two-level family exhibits a finite window in which coherence lowers entropy while preserving global Wigner positivity. A complementary construction repairs a remote negative tail with an exponentially small thermal admixture; an explicit mixing weight of $2\times10^{-21}$ preserves a rigorously established entropy decrease. Optimisation over all one-mode Wigner-nonnegative states gives the sharp low-energy scale $E^γ/[\ln(1/E)]^β$, with $γ\simeq0.7412$ and $β\simeq0.5861$. Because $γ<1$, tensor products can have vanishing total energy and trace distance from vacuum while their entropy deficit diverges. We derive the exact half-transmission threshold for universal Shannon-entropy recovery and connect it to companion results showing residual non-Gaussian structure. The counterexamples reveal distinct controls on entropy: coherence sets the local descent, mode number amplifies it, and loss restores the vacuum bound.
Source: arXiv (Cornell University)
Author: He, Zixuan
Institution: University of Glasgow
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213312420
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