---
res:
  bibo_abstract:
  - A defining feature of quantum many-body systems is the exponential scaling of
    the Hilbert space with the number of degrees of freedom. This exponential complexity
    naïvely renders a complete state characterization, for instance via the complete
    set of bipartite Renyi entropies for all disjoint regions, a challenging task.
    Recently, a compact way of storing subregions' purities by encoding them as amplitudes
    of a fictitious quantum wave function, known as entanglement feature, was proposed.
    Notably, the entanglement feature can be a simple object even for highly entangled
    quantum states. However the complexity and practical usage of the entanglement
    feature for general quantum states has not been explored. In this work, we demonstrate
    that the entanglement feature can be efficiently learned using only a polynomial
    amount of samples in the number of degrees of freedom through the so-called tensor
    cross interpolation (TCI) algorithm, assuming it is expressible as a finite bond
    dimension MPS. We benchmark this learning process on Haar and random MPS states,
    confirming analytic expectations. Applying the TCI algorithm to quantum eigenstates
    of various one dimensional quantum systems, we identify cases where eigenstates
    have entanglement feature learnable with TCI. We conclude with possible applications
    of the learned entanglement feature, such as quantifying the distance between
    different entanglement patterns and finding the optimal one-dimensional ordering
    of physical indices in a given state, highlighting the potential utility of the
    proposed purity interpolation method.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Dmytro
      foaf_name: Kolisnyk, Dmytro
      foaf_surname: Kolisnyk
      foaf_workInfoHomepage: http://www.librecat.org/personId=530a7320-5355-11ee-ae5a-82a46997aaa7
    orcid: 0000-0002-8612-8202
  - foaf_Person:
      foaf_givenName: Raimel A
      foaf_name: Medina Ramos, Raimel A
      foaf_surname: Medina Ramos
      foaf_workInfoHomepage: http://www.librecat.org/personId=CE680B90-D85A-11E9-B684-C920E6697425
    orcid: 0000-0002-5383-2869
  - foaf_Person:
      foaf_givenName: Romain
      foaf_name: Vasseur, Romain
      foaf_surname: Vasseur
  - foaf_Person:
      foaf_givenName: Maksym
      foaf_name: Serbyn, Maksym
      foaf_surname: Serbyn
      foaf_workInfoHomepage: http://www.librecat.org/personId=47809E7E-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-2399-5827
  bibo_doi: 10.22331/q-2026-05-22-2114
  bibo_volume: 10
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2521-327X
  dct_language: eng
  dct_publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften@
  dct_title: Tensor cross interpolation of purities in quantum many-body systems@
...