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Multipartite Entanglement in Stabilizer Tensor Networks.

Sepehr Nezami1,2, Michael Walter1,3

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Multipartite entanglement in quantum systems is challenging. This study reveals that stabilizer tensor networks, crucial for quantum gravity, exhibit scarce tripartite entanglement, limiting higher-order multipartite structures.

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Area of Science:

  • Quantum Information Theory
  • Quantum Many-Body Systems
  • Quantum Gravity

Background:

  • Understanding multipartite entanglement in quantum systems is limited, primarily focusing on bipartite entanglement.
  • Defining and quantifying multipartite entanglement in general quantum states remains a significant challenge.
  • Stabilizer tensor networks are a tractable class of quantum states with relevance to quantum gravity and AdS/CFT.

Purpose of the Study:

  • To initiate the study of multipartite entanglement within stabilizer tensor networks.
  • To investigate the relationship between the geometry of tensor networks and their multipartite entanglement structure.
  • To explore the implications of multipartite entanglement in stabilizer tensor networks for quantum gravity and quantum information.

Main Methods:

  • Analysis of generic stabilizer tensor networks to understand their multipartite entanglement.
  • Development of a spin model for evaluating the average Greenberger-Horne-Zeilinger (GHZ) triple content.
  • Derivation of a novel formula for the third moment of random stabilizer states.

Main Results:

  • The geometry of stabilizer tensor networks dictates their multipartite entanglement properties.
  • Average number of extractable Greenberger-Horne-Zeilinger (GHZ) triples is small, indicating scarce tripartite entanglement.
  • Higher-partite entanglement structures are restricted by the scarcity of tripartite entanglement.

Conclusions:

  • Stabilizer tensor networks offer a framework to study multipartite entanglement, revealing its scarcity.
  • Results provide a new operational interpretation of the monogamy of Ryu-Takayanagi mutual information.
  • An entropic diagnostic for higher-partite entanglement is proposed, with potential applications in quantum information.