Modular Krylov Complexity as a Boundary Probe of Area Operator and Entanglement Islands

• URL: http://arxiv.org/abs/2602.02675v1
• Date: Mon, 02 Feb 2026 19:00:24 GMT
• Title: Modular Krylov Complexity as a Boundary Probe of Area Operator and Entanglement Islands
• Authors: Niloofar Vardian,
• Abstract summary: We show that the area operator of a quantum extremal surface can be reconstructed directly from boundary dynamics without reference to bulk geometry.<n>Our results establish modular Krylov complexity as a concrete and computable probe of emergent spacetime geometry.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the area operator of a quantum extremal surface can be reconstructed directly from boundary dynamics without reference to bulk geometry. Our approach combines the operator-algebra quantum error-correction (OAQEC) structure of AdS/CFT with modular Krylov complexity. Using Lanczos coefficients of boundary modular dynamics, we extract the spectrum of the modular Hamiltonian restricted to the algebra of the entanglement wedge and isolate its central contribution, which is identified with the area operator. The construction is purely boundary-based and applies to superpositions of semiclassical geometries as well. As an application, we diagnose island formation and the Page transition in evaporating black holes using boundary modular evolution alone, bypassing any bulk extremization. More broadly, our results establish modular Krylov complexity as a concrete and computable probe of emergent spacetime geometry, providing a new route to accessing black hole interiors from boundary quantum dynamics.

Related papers

• Spectroscopic Search for Topological Protection in Open Quantum Hardware: The Dissipative Mixed Hodge Module Approach [0.0]
  Standard protocols model the dynamics of open quantum systems as a superposition of isolated, exponentially decaying eigenmodes.<n>We resolve this ambiguity by introducing a geometric framework based on textitDissipative Mixed Hodge Modules (DMHM)<n>We demonstrate that WFS acts as a dissipative x-ray, quantifying dissipative leakage in molecular polaritons and certifying topological isolation in Non-Hermitian Aharonov-Bohm rings.
  arXiv  Detail & Related papers  (2025-12-25T13:06:42Z)
• Unveiling non-Hermitian band structures with non-Bloch supercells [23.45255537572689]
  Non-Hermitian systems exhibit complex band structures where both energy and momentum have imaginary parts.<n>We introduce a non-Bloch supercell framework designed to overcome this challenge by decoupling Bloch phase control from the imaginary part of momentum.
  arXiv  Detail & Related papers  (2025-10-23T03:18:23Z)
• Programmable Exploration of Magnetic States in Lieb-Kagome Interpolated Lattices [44.99833362998488]
  A quantum annealer is used to simulate magnetic interactions in molecular qubit lattices inspired by experimentally realizable systems.<n>The annealer provides access to observables such as the static structure factor and magnetization over a wide parameter space.<n>This framework defines a modular and scalable paradigm for probing the limits of engineered quantum matter across chemistry, condensed matter, and quantum information science.
  arXiv  Detail & Related papers  (2025-07-24T21:47:54Z)
• Gapped Boundaries of Kitaev's Quantum Double Models: A Lattice Realization of Anyon Condensation from Lagrangian Algebras [9.780323665238711]
  We propose a systematic framework for constructing all gapped boundaries of Kitaev's quantum double models.<n>Generalizing this insight to the boundary, we derive the consistency condition for boundary ribbon operators.<n>Our construction provides a microscopic characterization of the bulk-to-boundary anyon condensation dynamics.
  arXiv  Detail & Related papers  (2025-04-28T06:22:06Z)
• Minimal Areas from Entangled Matrices [41.94295877935867]
  We show how entanglement entropy can be given as a minimisation, exhibiting many similarities to the Ryu-Takayanagi formula.<n>Our construction brings together the physics of entanglement edge modes, noncommutative geometry and quantum internal reference frames.<n>We find that coarse-graining is essential in our microscopic derivation, in order to control the proliferation of highly curved and disconnected non-geometric subregions in the sum.
  arXiv  Detail & Related papers  (2024-08-09T18:00:03Z)
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue [68.8204255655161]
  We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime. We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
  arXiv  Detail & Related papers  (2022-12-02T18:28:23Z)
• The frustration-free fully packed loop model [4.965221313169878]
  We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace. We show that the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
  arXiv  Detail & Related papers  (2022-06-03T18:00:04Z)
• Scaling limits of lattice quantum fields by wavelets [62.997667081978825]
  The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field.
  arXiv  Detail & Related papers  (2020-10-21T16:30:06Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• Quantum field theory with dynamical boundary conditions and the Casimir effect [0.0]
  We study a coupled system that describes the interacting dynamics between a bulk field, confined to a finite region with timelike boundary, and a boundary observable. We cast our classical system in the form of an abstract linear Klein-Gordon equation, in an enlarged Hilbert space for the bulk field and the boundary observable. Specifically, we compute the renormalized local state polarization and the local Casimir energy, which we can define for both the bulk field and the boundary observable of our system.
  arXiv  Detail & Related papers  (2020-04-12T16:27:16Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.