Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition

• URL: http://arxiv.org/abs/2512.22997v1
• Date: Sun, 28 Dec 2025 16:51:19 GMT
• Title: Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition
• Authors: Pawel Caputa, Abhigyan Saha, Piotr Sułkowski,
• Abstract summary: We introduce generalisations of von Neumann entanglement entropy that are invariant with respect to certain scale transformations.<n>These constructions are based on Unit-Invariant Singular Value Decomposition (UISVD) with its right-, left-, and bi-invariant incarnations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce generalisations of von Neumann entanglement entropy that are invariant with respect to certain scale transformations. These constructions are based on Unit-Invariant Singular Value Decomposition (UISVD) with its right-, left-, and bi-invariant incarnations, which itself are variations of the standard Singular Value Decomposition (SVD) that remain invariant under (appropriate set of) diagonal transformations. These measures are naturally defined for non-Hermitian or rectangular operators and remain useful when the input and output spaces possess different dimensions or metric weights. We apply the UISVD entropy and discuss its advantages in the physically interesting framework of Biorthogonal Quantum Mechanics, whose important aspect is indeed the behavior under scale transformations. Further, we illustrate features of UISVD-based entropies in other representative settings, from simple quantum mechanical bipartite states to random matrices relevant to quantum chaos and holography, and in the context of Chern-Simons theory. In all cases, the UISVD yields stable, physically meaningful entropic spectra that are invariant under rescalings and normalisations.

Related papers

• Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation [56.361076943802594]
  CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.
  arXiv  Detail & Related papers  (2026-02-16T18:58:55Z)
• WUSH: Near-Optimal Adaptive Transforms for LLM Quantization [52.77441224845925]
  Quantization to low bitwidth is a standard approach for deploying large language models.<n>A few extreme weights and activations stretch the dynamic range and reduce the effective resolution of the quantizer.<n>We derive, for the first time, closed-form optimal linear blockwise transforms for joint weight-activation quantization.
  arXiv  Detail & Related papers  (2025-11-30T16:17:34Z)
• Entropy Measures for Transition Matrices in Random Systems [0.7373617024876725]
  We show that only the distillation interpretation of ABB entropy corresponds to the joint success probability of distilling entanglement between the two quantum states used to construct the transition matrix.<n>Across all cases considered, the SVD and ABB entropies of the transition matrix closely mirror the behavior of the subsystem entanglement entropy of a single random state.
  arXiv  Detail & Related papers  (2025-08-12T18:04:55Z)
• Generalized Linear Mode Connectivity for Transformers [87.32299363530996]
  A striking phenomenon is linear mode connectivity (LMC), where independently trained models can be connected by low- or zero-loss paths.<n>Prior work has predominantly focused on neuron re-ordering through permutations, but such approaches are limited in scope.<n>We introduce a unified framework that captures four symmetry classes: permutations, semi-permutations, transformations, and general invertible maps.<n>This generalization enables, for the first time, the discovery of low- and zero-barrier linear paths between independently trained Vision Transformers and GPT-2 models.
  arXiv  Detail & Related papers  (2025-06-28T01:46:36Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells)<n>Our winding number is invariant under unitary or similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC [0.0]
  We show that a notion of entropy differences can be rigorously defined in quantum field theory in a general curved spacetime. We introduce a novel, covariant regulator for the entropy based on the modular crossed product. This regulator associates a type II von Neumann algebra to each spacetime subregion, resulting in well-defined renormalized entropies.
  arXiv  Detail & Related papers  (2023-12-12T18:07:13Z)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• On the Stability of Expressive Positional Encodings for Graphs [46.967035678550594]
  Using Laplacian eigenvectors as positional encodings faces two fundamental challenges. We introduce Stable and Expressive Positional generalizations (SPE) SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions.
  arXiv  Detail & Related papers  (2023-10-04T04:48:55Z)
• Covariant operator bases for continuous variables [0.0]
  We work out an alternative basis consisting of monomials on the basic observables, with the crucial property of behaving well under symplectic transformations. Given the density matrix of a state, the expansion coefficients in that basis constitute the multipoles, which describe the state in a canonically covariant form that is both concise and explicit.
  arXiv  Detail & Related papers  (2023-09-18T18:00:15Z)
• Equivariant Graph Mechanics Networks with Constraints [83.38709956935095]
  We propose Graph Mechanics Network (GMN) which is efficient, equivariant and constraint-aware. GMN represents, by generalized coordinates, the forward kinematics information (positions and velocities) of a structural object. Extensive experiments support the advantages of GMN compared to the state-of-the-art GNNs in terms of prediction accuracy, constraint satisfaction and data efficiency.
  arXiv  Detail & Related papers  (2022-03-12T14:22:14Z)
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system [0.0]
  We study a non-Hermitian, non-interacting model of fermions which is invariant under combined $PT$ transformation. Our models show a phase transition from $PT$ unbroken phase to broken phase as we tune the hermiticity breaking parameter.
  arXiv  Detail & Related papers  (2021-02-01T19:00:08Z)
• Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States [1.2891210250935143]
  We study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices. Specifically, we obtain in generic form the differential equations for the covariance matrix, the mean values, and the density matrix parameters of a multipartite Gaussian state. The resulting nonlinear equations are used to solve the dynamics of the system instead of the Schr"odinger equation.
  arXiv  Detail & Related papers  (2020-05-23T09:11:51Z)

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.