---
APC_amount: 4863,6 EUR
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '17493'
abstract:
- lang: eng
  text: 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.
acknowledgement: B. V. acknowledges funding from the Austrian Science Foundation (Grant
  No. FWF, P 32597 N), from the French National Research Agency via the JCJC project
  QRand (Grant No. ANR-20-CE47-0005), and via the research programs Plan France 2030
  EPIQ (Grant No. ANR-22-PETQ-0007), QUBITAF (Grant No. ANR-22-PETQ-0004), and HQI
  (Grant No. ANR-22-PNCQ-0002). M. L. and M. S. acknowledge support by the European
  Research Council under the European Union’s Horizon 2020 research and innovation
  program (Grant Agreement No. 850899). M. S. acknowledges the hospitality of KITP
  supported in part by the National Science Foundation under Grants No. NSF PHY-1748958
  and No. NSF PHY-2309135. J. I. C. is supported by the Hightech Agenda Bayern Plus
  through the Munich Quantum Valley and the German Federal Ministry of Education and
  Research through EQUAHUMO (Grant No. 13N16066). P. Z. acknowledges funding from
  the European Union’s Horizon 2020 research and innovation program under Grant Agreement
  No. 101113690 (PASQuanS2.1).
article_number: '031035'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Benoît
  full_name: Vermersch, Benoît
  last_name: Vermersch
- first_name: Marko
  full_name: Ljubotina, Marko
  id: F75EE9BE-5C90-11EA-905D-16643DDC885E
  last_name: Ljubotina
  orcid: 0000-0003-0038-7068
- first_name: J. Ignacio
  full_name: Cirac, J. Ignacio
  last_name: Cirac
- first_name: Peter
  full_name: Zoller, Peter
  last_name: Zoller
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
- first_name: Lorenzo
  full_name: Piroli, Lorenzo
  last_name: Piroli
citation:
  ama: Vermersch B, Ljubotina M, Cirac JI, Zoller P, Serbyn M, Piroli L. Many-body
    entropies and entanglement from polynomially many local measurements. <i>Physical
    Review X</i>. 2024;14(3). doi:<a href="https://doi.org/10.1103/physrevx.14.031035">10.1103/physrevx.14.031035</a>
  apa: Vermersch, B., Ljubotina, M., Cirac, J. I., Zoller, P., Serbyn, M., &#38; Piroli,
    L. (2024). Many-body entropies and entanglement from polynomially many local measurements.
    <i>Physical Review X</i>. American Physical Society. <a href="https://doi.org/10.1103/physrevx.14.031035">https://doi.org/10.1103/physrevx.14.031035</a>
  chicago: Vermersch, Benoît, Marko Ljubotina, J. Ignacio Cirac, Peter Zoller, Maksym
    Serbyn, and Lorenzo Piroli. “Many-Body Entropies and Entanglement from Polynomially
    Many Local Measurements.” <i>Physical Review X</i>. American Physical Society,
    2024. <a href="https://doi.org/10.1103/physrevx.14.031035">https://doi.org/10.1103/physrevx.14.031035</a>.
  ieee: B. Vermersch, M. Ljubotina, J. I. Cirac, P. Zoller, M. Serbyn, and L. Piroli,
    “Many-body entropies and entanglement from polynomially many local measurements,”
    <i>Physical Review X</i>, vol. 14, no. 3. American Physical Society, 2024.
  ista: Vermersch B, Ljubotina M, Cirac JI, Zoller P, Serbyn M, Piroli L. 2024. Many-body
    entropies and entanglement from polynomially many local measurements. Physical
    Review X. 14(3), 031035.
  mla: Vermersch, Benoît, et al. “Many-Body Entropies and Entanglement from Polynomially
    Many Local Measurements.” <i>Physical Review X</i>, vol. 14, no. 3, 031035, American
    Physical Society, 2024, doi:<a href="https://doi.org/10.1103/physrevx.14.031035">10.1103/physrevx.14.031035</a>.
  short: B. Vermersch, M. Ljubotina, J.I. Cirac, P. Zoller, M. Serbyn, L. Piroli,
    Physical Review X 14 (2024).
date_created: 2024-09-04T18:57:11Z
date_published: 2024-08-26T00:00:00Z
date_updated: 2025-09-08T09:04:14Z
day: '26'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.1103/physrevx.14.031035
ec_funded: 1
external_id:
  arxiv:
  - '2311.08108'
  isi:
  - '001299667100002'
file:
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  checksum: 1b114acc89025120727200681e4e9074
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  creator: cchlebak
  date_created: 2024-09-05T09:39:00Z
  date_updated: 2024-09-05T09:39:00Z
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file_date_updated: 2024-09-05T09:39:00Z
fulldoi: https://doi.org/10.1103/physrevx.14.031035
has_accepted_license: '1'
intvolume: '        14'
isi: 1
issue: '3'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
  call_identifier: H2020
  grant_number: '850899'
  name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication: Physical Review X
publication_identifier:
  issn:
  - 2160-3308
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Many-body entropies and entanglement from polynomially many local measurements
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  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 14
year: '2024'
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