License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.22
URN: urn:nbn:de:0030-drops-124298
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12429/
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Cai, Jin-Yi ; Fu, Zhiguo ; Shao, Shuai

From Holant to Quantum Entanglement and Back

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LIPIcs-ICALP-2020-22.pdf (0.6 MB)

Abstract

Holant problems are intimately connected with quantum theory as tensor networks. We first use techniques from Holant theory to derive new and improved results for quantum entanglement theory. We discover two particular entangled states |Ψ₆⟩ of 6 qubits and |Ψ₈⟩ of 8 qubits respectively, that have extraordinary closure properties in terms of the Bell property. Then we use entanglement properties of constraint functions to derive a new complexity dichotomy for all real-valued Holant problems containing a signature of odd arity. The signatures need not be symmetric, and no auxiliary signatures are assumed.

BibTeX - Entry

@InProceedings{cai_et_al:LIPIcs:2020:12429,
  author =	{Jin-Yi Cai and Zhiguo Fu and Shuai Shao},
  title =	{{From Holant to Quantum Entanglement and Back}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12429},
  URN =		{urn:nbn:de:0030-drops-124298},
  doi =		{10.4230/LIPIcs.ICALP.2020.22},
  annote =	{Keywords: Holant problem, Quantum entanglement, SLOCC equivalence, Bell property}
}

Keywords: Holant problem, Quantum entanglement, SLOCC equivalence, Bell property
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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