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Cited by 16Quantum many-body systemsQuantum Information and CryptographyQuantum Mechanics and Applications

The DOI matches its Crossref record; 29 of the 30 references it cites were found in a registry or an index.

Invariant perfect tensors

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Li, Youning, Han, Muxin, Grassl, Markus, Zeng, Bei·2017·New Journal of Physics
DOI 10.1088/1367-2630/aa7235
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Abstract

Invariant tensors are states in the SU(2) tensor product representation that are invariant under SU(2) action. They play an important role in the study of loop quantum gravity. On the other hand, perfect tensors are highly entangled many-body quantum states with local density matrices maximally mixed. Recently, the notion of perfect tensors has attracted a lot of attention in the fields of quantum information theory, condensed matter theory, and quantum gravity. In this work, we introduce the concept of an invariant perfect tensor (IPT), which is an n -valent tensor that is both invariant and perfect. We discuss the existence and construction of IPTs. For bivalent tensors, the IPT is the unique singlet state for each local dimension. The trivalent IPT also exists and is uniquely given by Wigner's symbol. However, we show that, surprisingly, 4-valent IPTs do not exist for any identical local dimension d . On the contrary, when the dimension is large, almost all invariant tensors are asymptotically perfect, which is a consequence of the phenomenon of the concentration of measure for multipartite quantum states.

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Crossref · 10.1088/1367-2630/aa7235

Cites

29 of 29 references verified0 citation errors · 0 not checkable

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  • SU(2)-invariant absolutely maximally entangled states do not exist.

    “In this section, we show that SU(2)-invariant AME states (equivalently invariant perfect tensors [13]), which are necessary for a LQG equivalent to the toy models for the AdS/CFT correspondence in [6], do not exist.”

    From Hyperinvariant spin network states — an AdS/CFT model from first principles (2026) · cites this paper as [13]

  • No-go theorems for Werner states, SU(2) intertwiners with valence four or local dimension two can be understood in a more general context of a no-go result for covariant codes and from lower bounds for the infidelity of recovery.

    “Nogo theorems for Werner states [11,12], SU(2) intertwiners with valence four [13] or local dimension two [14] can be understood in a more general context of a no-go result for covariant codes [15] and from lower bounds for the infidelity of recovery [16].”

    From Hyperinvariant spin network states — an AdS/CFT model from first principles (2026) · cites this paper as [13]

Citations

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1 of the 30 references couldn’t be matched to a known paper.

Research works printed but not linked: 1

  1. Minkowski H, 1989, Ausgewählte Arbeiten zur Zahlentheorie und zur Geometrie (Teubner-Archiv zur Mathematik), 12

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Metadata

Authors
Li, Y., Han, M., Grassl, M., & Zeng, B.
Affiliations
  • Collaborative Innovation Center of Quantum Matter (CN)
  • Friedrich-Alexander-Universität Erlangen-Nürnberg (DE)
  • University of Waterloo (CA)
Corresponding author
Li, Youning
ORCID
Venue
New Journal of Physics
Publisher
IOP Publishing
Published
2017-06-26
Volume
19
Issue
6
Pages
063029
ISSN
1367-2630 (ISSN-L)
DOI
10.1088/1367-2630/aa7235
OpenAlex
W2564335334
Cited by
15
References
30
Citations by year
2026: 1 · 2024: 2 · 2023: 3 · 2022: 1 · 2020: 3 · 2019: 3 · 2018: 1 · 2017: 1
FWCI
1.07
Type
journal article
Language
en
Open access
Licence
Locations
  • New Journal of Physics (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • Max Planck Digital Library (submittedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
  • Rare & Special e-Zone (The Hong Kong University of Science and Technology) (submittedVersion)
  • OPUS FAU (Kooperativer Bibliotheksverbund Berlin-Brandenburg (KOBV), on behalf of the Universitätsbibliothek Erlangen-Nürnberg) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
National Natural Science Foundation of China (J1310023)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
invariant tensors, loop quantum gravity, singlet state, Wigner 3j symbols, concentration of measure, multipartite entanglement

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