Complexity of fermionic states

• URL: http://arxiv.org/abs/2306.07584v2
• Date: Tue, 5 Mar 2024 07:13:03 GMT
• Title: Complexity of fermionic states
• Authors: Tuomas I. Vanhala and Teemu Ojanen
• Abstract summary: We define the complexity of a particle-conserving many-fermion state as the entropy of its Fock space probability distribution. Our work has fundamental implications on how much information is encoded in fermionic states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: How much information a fermionic state contains? To address this fundamental question, we define the complexity of a particle-conserving many-fermion state as the entropy of its Fock space probability distribution, minimized over all Fock representations. The complexity characterizes the minimum computational and physical resources required to represent the state and store the information obtained from it by measurements. Alternatively, the complexity can be regarded a Fock space entanglement measure describing the intrinsic many-particle entanglement in the state. We establish universal lower bound for the complexity in terms of the single-particle correlation matrix eigenvalues and formulate a finite-size complexity scaling hypothesis. Remarkably, numerical studies on interacting lattice models suggest a general model-independent complexity hierarchy: ground states are exponentially less complex than average excited states which, in turn, are exponentially less complex than generic states in the Fock space. Our work has fundamental implications on how much information is encoded in fermionic states.

Related papers

• Phase-space complexity of discrete-variable quantum states and operations [0.0]
  We introduce a quantifier of phase-space complexity for discrete-variable quantum systems.<n>The complexity is normalized such that coherent states have unit complexity, while the completely mixed state has zero complexity.<n>We extend the framework to quantum channels, defining measures for both the generation and breaking of complexity.
  arXiv  Detail & Related papers  (2026-03-03T19:00:02Z)
• Gaussian fermionic embezzlement of entanglement [41.321581612257056]
  We show that the embezzling property is in fact a generic property of fermionic Gaussian states.<n>We bridge finite-size systems to abstract characterizations based on the classification of von Neumann algebras.
  arXiv  Detail & Related papers  (2025-09-19T08:26:03Z)
• Loss-Complexity Landscape and Model Structure Functions [56.01537787608726]
  We develop a framework for dualizing the Kolmogorov structure function $h_x(alpha)$.<n>We establish a mathematical analogy between information-theoretic constructs and statistical mechanics.<n>We explicitly prove the Legendre-Fenchel duality between the structure function and free energy.
  arXiv  Detail & Related papers  (2025-07-17T21:31:45Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation. We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue. We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• The Large-Scale Structure of Entanglement in Quantum Many-body Systems [44.99833362998488]
  We show that the thermodynamic limit of a many-body system can reveal entanglement properties that are hard to detect in finite-size systems. In particular, we show that every gapped phase of matter, even the trivial one, in $Dgeq 2$ dimensions contains models with the strongest possible bipartite large-scale entanglement.
  arXiv  Detail & Related papers  (2025-03-05T19:01:05Z)
• On the Complexity of Quantum Field Theory [0.0]
  We show that from minimal assertions, one is naturally led to measure complexity by two integers, called format and degree. We discuss the physical interpretation of our approach in the context of perturbation theory, symmetries, and the renormalization group.
  arXiv  Detail & Related papers  (2024-10-30T18:00:00Z)
• Entanglement entropy bounds for pure states of rapid decorrelation [0.0]
  We construct high fidelity approximations of relatively low complexity for pure states of quantum lattice systems. The applicability of the general results is demonstrated on the quantum Ising model in transverse field. We establish an area-law type bound on the entanglement in the model's subcritical ground states, valid in all dimensions and up to the model's quantum phase transition.
  arXiv  Detail & Related papers  (2024-06-14T17:28:03Z)
• Complexity-constrained quantum thermodynamics [0.2796197251957244]
  We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state's complexity entropy. The complexity entropy quantifies a trade-off between the work cost and complexity cost of resetting a state. We identify information-theoretic applications of the complexity entropy.
  arXiv  Detail & Related papers  (2024-03-07T19:00:01Z)
• Strongly subradiant states in planar atomic arrays [39.58317527488534]
  We study collective dipolar oscillations in finite planar arrays of quantum emitters in free space. We show that the external coupling between the collective states associated with the symmetry of the array and with the quasi-flat dispersion of the corresponding infinite lattice plays a crucial role in the boost of their radiative lifetime.
  arXiv  Detail & Related papers  (2023-10-10T17:06:19Z)
• Krylov Complexity of Fermionic and Bosonic Gaussian States [9.194828630186072]
  This paper focuses on emphKrylov complexity, a specialized form of quantum complexity. It offers an unambiguous and intrinsically meaningful assessment of the spread of a quantum state over all possible bases.
  arXiv  Detail & Related papers  (2023-09-19T07:32:04Z)
• Probing multipartite entanglement through persistent homology [6.107978190324034]
  We propose a study of multipartite entanglement through persistent homology. persistent homology is a tool used in topological data analysis. We show that persistence barcodes provide more fine-grained information than its topological summary.
  arXiv  Detail & Related papers  (2023-07-14T17:24:33Z)
• Local Intrinsic Dimensional Entropy [29.519376857728325]
  Most entropy measures depend on the spread of the probability distribution over the sample space $mathcalX|$. In this work, we question the role of cardinality and distribution spread in defining entropy measures for continuous spaces. We find that the average value of the local intrinsic dimension of a distribution, denoted as ID-Entropy, can serve as a robust entropy measure for continuous spaces.
  arXiv  Detail & Related papers  (2023-04-05T04:36:07Z)
• DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion [66.21290235237808]
  We introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks.
  arXiv  Detail & Related papers  (2023-01-23T15:18:54Z)
• Krylov complexity in quantum field theory, and beyond [44.99833362998488]
  We study Krylov complexity in various models of quantum field theory. We find that the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos.
  arXiv  Detail & Related papers  (2022-12-29T19:00:00Z)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

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.