---
res:
  bibo_abstract:
  - "Consider a bipartite quantum system, where Alice and Bob jointly possess\r\na
    pure state |ψ\x02. Using local quantum operations on their respective subsystems,
    and\r\nunlimited classical communication, Alice and Bob may be able to transform
    |ψ\x02 into\r\nanother state |φ\x02. Famously, Nielsen’s theorem [28] provides
    a necessary and sufficient\r\nalgebraic criterion for such a transformation to
    be possible (namely, the entanglement\r\nspectrum of |φ\x02 should majorise the
    entanglement spectrum of |ψ\x02). In the paper where\r\nNielsen proved this theorem,
    he conjectured that in the limit of large dimensionality, for\r\nalmost all pairs
    of states |ψ\x02, |φ\x02 (according to the natural unitary invariant measure)
    such\r\na transformation is not possible. That is to say, typical pairs of quantum
    states |ψ\x02, |φ\x02\r\nare entangled in fundamentally different ways, that cannot
    be converted to each other via\r\nlocal operations and classical communication.ViaNielsen’s
    theorem, this conjecture can\r\nbe equivalently stated as a conjecture about majorisation
    of spectra of random matrices\r\nfrom the so-called trace-normalised complex Wishart–Laguerre
    ensemble. Concretely,\r\nlet X and Y be independent n × m random matrices whose
    entries are i.i.d. standard\r\ncomplex Gaussians; then Nielsen’s conjecture says
    that the probability that the spectrum\r\nof XX†/ tr(XX†) majorises the spectrum
    of YY†/ tr(YY†) tends to zero as both n and\r\nm grow large. We prove this conjecture,
    and we also confirm some related predictions\r\nof Cunden et al. [12].@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Vishesh
      foaf_name: Jain, Vishesh
      foaf_surname: Jain
  - foaf_Person:
      foaf_givenName: Matthew Alan
      foaf_name: Kwan, Matthew Alan
      foaf_surname: Kwan
      foaf_workInfoHomepage: http://www.librecat.org/personId=5fca0887-a1db-11eb-95d1-ca9d5e0453b3
    orcid: 0000-0002-4003-7567
  - foaf_Person:
      foaf_givenName: Marcus
      foaf_name: Michelen, Marcus
      foaf_surname: Michelen
  bibo_doi: 10.1007/s00220-026-05711-4
  bibo_issue: '10'
  bibo_volume: 407
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0010-3616
  - http://id.crossref.org/issn/1432-0916
  dct_language: eng
  dct_publisher: Springer@
  dct_title: Entangled states are typically incomparable@
  fabio_hasPubmedId: '42668663'
...