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More on genuine multientropy and holography

Norihiro Iizuka1,2,*, Simon Lin3,†, and Mitsuhiro Nishida4,‡

  • *Contact author: iizuka@phys.nthu.edu.tw
  • †Contact author: simonlin@nyu.edu
  • ‡Contact author: mnishida124@gmail.com
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Phys. Rev. D 112, 066014 – Published 22 September, 2025

DOI: https://doi.org/10.1103/x76v-mr6n

Abstract

By generalizing the construction of genuine multientropy GM(q) for genuine multipartite entanglement proposed in the previous paper [Genuine multi-entropy and holography, Phys. Rev. D 112, 026011 (2025).], we give a prescription on how to construct GM(q) systematically for any q. The crucial point is that our construction naturally fits to the partition number p(a) of integer a. For general q, GM(q) contains N(q)=p(q)−p(q−1)−1 number of free parameters. Furthermore, these give N(q)+1 number of new diagnostics for genuine q-partite entanglement. Especially for q=4 case, this reproduces not only the known diagnostics pointed out by Balasubramanian et al. [Multiboundary wormholes and holographic entanglement, Classical Quantum Gravity 31, 185015 (2014).], but also a new diagnostics for quadripartite entanglement. We also study these GM(q) for q=4, 5 in holography and show that these are of the order of O(1/GN) both analytically and numerically. Our results give evidence that genuine multipartite entanglement is ubiquitous in holography. We discuss the connection to quantum error correction and the role of genuine multipartite entanglement in bulk reconstruction.

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Phys. Rev. D 112, 066014– Published 22 September, 2025
  • Received 10 June 2025
  • Accepted 22 August 2025
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