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Genuine multientropy, dihedral invariants, and Lifshitz theory

Clément Berthière* and Paul Gaudin†

  • *Contact author: clement.berthiere@irsamc.ups-tlse.fr
  • †Contact author: paul.gaudin@irsamc.ups-tlse.fr
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Phys. Rev. D 113, 065029 – Published 30 March, 2026

DOI: https://doi.org/10.1103/vcqd-rkmn

Abstract

Multi-invariants are local-unitary invariants of state replicas introduced as potential probes of multipartite entanglement and correlations in quantum many-body systems. In this paper, we investigate two multi-invariants for tripartite pure states, namely multientropy and dihedral invariant. We compute the (genuine) multientropy for Lifshitz ground states and obtain its analytical continuation to noninteger values of Rényi index. We show that the genuine multientropy can be expressed in terms of mutual information and logarithmic negativity, a relation that also holds for stabilizer states. For general tripartite pure states, we demonstrate that dihedral invariants are related to Rényi reflected entropies. In particular, we show that the dihedral permutations of replicas are equivalent to the reflected construction, or alternatively to the realignment of density matrices.

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Phys. Rev. D 113, 065029– Published 30 March, 2026
  • Received 24 November 2025
  • Accepted 14 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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