An asymmetry lower bound on fermionic non-Gaussianity

• URL: http://arxiv.org/abs/2603.16762v1
• Date: Tue, 17 Mar 2026 16:42:34 GMT
• Title: An asymmetry lower bound on fermionic non-Gaussianity
• Abstract summary: We relate measures of non-Gaussianity with the Shannon entropy of the particle-number distribution.<n>We derive a lower bound on the relative entropy of non-Gaussianity in terms of the exponential of the Shannon entropy.<n>Our results can be viewed as a practical way to lower bound non-Gaussianity, highlighting a non-trivial interplay with particle-number asymmetry.
• Score: 0.21111026813272182
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fermionic Gaussian states are a fundamental tool in many-body physics, faithfully representing non-interacting quantum systems and allowing for efficient numerical simulations. Given a many-body wave function, it is therefore interesting to ask how much it differs from that of a Gaussian state, as quantified by the notion of non-Gaussianity. In this work, we relate measures of non-Gaussianity with the Shannon entropy of the particle-number distribution, coinciding with the particle-number asymmetry for pure states. We derive a lower bound on the relative entropy of non-Gaussianity in terms of the exponential of the Shannon entropy, and study numerically its tightness for large system sizes. Our bound is non-trivial for large values of the asymmetry and relies on the concentration of the particle-number distribution of (mixed) fermionic Gaussian states. Since the Shannon entropy of the particle-number distribution is often efficient to compute or experimentally measure, our results can be viewed as a practical way to lower bound non-Gaussianity, highlighting a non-trivial interplay with particle-number asymmetry.

Related papers

• Energetics of non-Gaussianity in single mode cavities [0.0]
  Non-Gaussian states play a central role in quantum technologies.<n>We introduce an energetic framework to characterize non-Gaussianity in single-mode bosonic states.
  arXiv  Detail & Related papers  (2026-06-30T05:23:29Z)
• Non-Gaussianity of random quantum states [0.2621730497733947]
  We study the fermionic non-Gaussianity in typical quantum states, focusing on Haar random states of qubits with or without a global $U(1)$ symmetry.<n>We derive analytical predictions for the non-Gaussianity, defined as the relative entropy between the reduced density matrix and its Gaussianized counterpart.<n>These results establish the typical scaling of fermionic non-Gaussianity in random states and analyze how this is modified by the presence of global symmetries.
  arXiv  Detail & Related papers  (2026-05-18T18:05:19Z)
• A Berry-Esseen Bound for Quantum Lattice Systems [33.82119899094064]
  We prove a version of the Berry-Esseen theorem for quantum lattice systems.<n>We provide a rigorous convergence estimate towards the normal distribution for large but finite system size.
  arXiv  Detail & Related papers  (2026-05-05T14:58:16Z)
• Optimal Discrimination of Gaussian States by Gaussian Measurements [9.157994196176551]
  We derive a condition that completely determines whether or not there exists an optimal Gaussian measurement achieving the max-relative entropy.<n>When the condition is not met, there is a strict gap between the distinguishability achievable by Gaussian measurements and the unconstrained max-relative entropy.
  arXiv  Detail & Related papers  (2026-03-12T17:12:33Z)
• Exploring the possibility of a complex-valued non-Gaussianity measure for quantum states of light [6.512809432683749]
  We introduce the differential relative entropy between any Wigner function and its Gaussian associate and we examine its potential as a non-Gaussianity measure. The proposed, phase-space based non-Gaussianity measure is complex-valued, with its imaginary part possessing the physical meaning of the negative volume of the Wigner function. At the same time, the real part of this measure provides an extra layer of information, rendering the complex-valued quantity a measure of non-Gaussianity.
  arXiv  Detail & Related papers  (2023-03-02T00:37:52Z)
• Dilute neutron star matter from neural-network quantum states [58.720142291102135]
  Low-density neutron matter is characterized by the formation of Cooper pairs and the onset of superfluidity. We model this density regime by capitalizing on the expressivity of the hidden-nucleon neural-network quantum states combined with variational Monte Carlo and reconfiguration techniques.
  arXiv  Detail & Related papers  (2022-12-08T17:55:25Z)
• Matched entanglement witness criteria for continuous variables [11.480994804659908]
  We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. This opens a way for precise detection of non-Gaussian entanglement.
  arXiv  Detail & Related papers  (2022-08-26T03:45:00Z)
• Fractional Quantum Zeno Effect Emerging from Non-Hermitian Physics [12.706932285002544]
  We predict quantum non-Hermitian phenomena: the fractional quantum Zeno (FQZ) effect and FQZ-induced photon antibunching. We find FQZ-induced strong photon antibunching in the steady state of a driven emitter even for weak nonlinearities. Remarkably, we identify that the sub-Poissonian quantum statistics of photons, which has no classical analogs, stems here from the key role of non-Hermiticity.
  arXiv  Detail & Related papers  (2022-07-07T17:41:24Z)
• Symmetry-resolved Page curves [0.0]
  We study a natural extension in the presence of a conservation law and introduce the symmetry-resolved Page curves. We derive explicit analytic formulae for two important statistical ensembles with a $U(1)$-symmetry.
  arXiv  Detail & Related papers  (2022-06-10T13:22:14Z)
• Quantifying non-Gaussianity of a quantum state by the negative entropy of quadrature distributions [0.0]
  We propose a non-Gaussianity measure of a multimode quantum state based on the negentropy of quadrature distributions. Our measure satisfies desirable properties as a non-Gaussianity measure.
  arXiv  Detail & Related papers  (2021-09-29T11:22:40Z)
• Dissipative evolution of quantum Gaussian states [68.8204255655161]
  We derive a new model of dissipative time evolution based on unitary Lindblad operators. As we demonstrate, the considered evolution proves useful both as a description for random scattering and as a tool in dissipator engineering.
  arXiv  Detail & Related papers  (2021-05-26T16:03:34Z)
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme [8.37609145576126]
  The relative entropy of entanglement $E_Rite is defined as the distance of a multi-part quantum entanglement from the set of separable states as measured by the quantum relative entropy. We show that this state is always achieved, i.e. any state admits a closest separable state, even in dimensions; also, $E_Rite is everywhere lower semi-negative $lambda_$quasi-probability distribution.
  arXiv  Detail & Related papers  (2021-05-17T18:03:02Z)
• Sample-efficient learning of quantum many-body systems [17.396274240172122]
  We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs state. We give the first sample-efficient algorithm for the quantum Hamiltonian learning problem.
  arXiv  Detail & Related papers  (2020-04-15T18:01:59Z)
• Schoenberg-Rao distances: Entropy-based and geometry-aware statistical Hilbert distances [12.729120803225065]
  We study a class of statistical Hilbert distances that we term the Schoenberg-Rao distances. We derive novel closed-form distances between mixtures of Gaussian distributions. Our method constitutes a practical alternative to Wasserstein distances and we illustrate its efficiency on a broad range of machine learning tasks.
  arXiv  Detail & Related papers  (2020-02-19T18:48:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.