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  Invariant Perfect Tensors

Li, Y., Han, M., Grassl, M., & Zeng, B. (2017). Invariant Perfect Tensors. New Journal of Physics, 19: 063029. doi:10.1088/1367-2630/aa7235.

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 Creators:
Li, Youning1, Author
Han, Muxin1, Author
Grassl, Markus2, Author           
Zeng, Bei1, Author
Affiliations:
1external, ou_persistent22              
2Quantumness, Tomography, Entanglement, and Codes, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society, ou_2364709              

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Free keywords: Quantum Physics, quant-ph, Condensed Matter, Strongly Correlated Electrons, cond-mat.str-el,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Abstract: Invariant tensors are states in the SU(2) tensor product representation that are invariant under the 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 recently 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 a $n$-valent tensor that is both invariant and perfect. We discuss the existence and construction of IPT. For bivalent tensors, the invariant perfect tensor is the unique singlet state for each local dimension. The trivalent invariant perfect tensor also exists and is uniquely given by Wigner's 3j symbol. However, we show that, surprisingly, there does not exist four-valent invariant perfect tensors for any dimension. On the contrary, when the dimension is large, almost all invariant tensors are perfect asymptotically, which is a consequence of the phenomenon of
concentration of measure for multipartite quantum states.

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Language(s): eng - English
 Dates: 2017-06-26
 Publication Status: Issued
 Pages: 16 pages, comment welcome
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 Table of Contents: -
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Title: New Journal of Physics
  Abbreviation : New J. Phys.
Source Genre: Journal
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Publ. Info: Bristol : IOP Publishing
Pages: - Volume / Issue: 19 Sequence Number: 063029 Start / End Page: - Identifier: ISSN: 1367-2630
CoNE: https://pure.mpg.de/cone/journals/resource/954926913666
DOI: 10.1088/1367-2630/aa7235