Many-Body Entropies and Entanglement from Polynomially Many Local Measurements
Year: 2024
Type: article
Abstract: Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical postprocessing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix, which allow us to reconstruct entropies and PT moments from information on local subsystems. This identification yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements providing a practical and common measurement scheme, we prove that our protocol requires only polynomially many measurements and postprocessing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators and provide numerical evidence that they are satisfied in more general, physically interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today’s quantum platforms. Published by the American Physical Society 2024
Source: Physical Review X
Institutions: Austrian Academy of Sciences, Universität Innsbruck, Institute for Quantum Optics and Quantum Information Innsbruck, Laboratoire de Physique et Modélisation des Milieux Condensés, Institute of Science and Technology Austria, Max Planck Institute of Quantum Optics, Munich Center for Quantum Science and Technology, Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, University of Bologna
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $4,200
Funders: National Science Foundation, European Commission, Agence Nationale de la Recherche, Bundesministerium für Bildung und Forschung, Austrian Science Fund, Horizon 2020 Framework Programme, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, H2020 European Research Council
Awards: G1190173965, G168288183, G1871477277, Programmable Atomic Large-scale Quantum Simulation 2 - SGA1, Etude de la pile quantique : Algorithmes, modèles de calcul et simulation pour l’informatique quantique, G2298275804, G2844252278, Initiative Nationale Hybride HPC Quantique – R&D et Support des communautés, G3398237449, Qubits à Atomes Froids pour la Simulation et le Calcul Quantiques, G434337789, G4689434848, Probing and verifying large-scale quantum technologies via randomized measurements, G4856404060, G5261598906, G5296751580, G5334593051, Kavli Institute for Theoretical Physics, G7182031487, G760448223, Kavli Institute for Theoretical Physics, G8679735702, G985207216
OpenAlex ID: W4401888748