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PreprintCC BY 4.0arXiv

Mixed-state extension of the holographic signal inequality

  • Joydeep Naskar
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Abstract

A novel inequality involving the residual information and genuine multi-entropy was proposed in \cite{Balasubramanian:2025hxg} for tripartite holographic pure states, using which it was argued, that purely GHZ-like tripartite entanglement is not allowed in holography. In this work, we generalize this holographic signal inequality to mixed states. In a minimal extension, we compute the reflected genuine multi-entropy following \cite{Yuan:2024yfg} and find a class of holographic geometries that violate this minimally extended inequality due to a vanishing Markov gap. We can symmetrize this prescription, where instead of computing the residual information on the given mixed state ρABC, we compute it on its canonical purification. The inequality is restored on the canonically purified state. Finally, we conjecture a new inequality for tripartite holographic states and give supporting evidence.

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Cite

BibTeXRIS
BibTeX
@misc{naskar2026mixedstate,
  title = {{Mixed-state extension of the holographic signal inequality}},
  author = {Joydeep Naskar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.26617},
  eprint = {2605.26617},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.26617},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Mixed-state extension of the holographic signal inequality
AU  - Joydeep Naskar
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2605.26617
UR  - https://arxiv.org/abs/2605.26617
AB  - A novel inequality involving the residual information and genuine multi-entropy was proposed in \cite{Balasubramanian:2025hxg} for tripartite holographic pure states, using which it was argued, that purely GHZ-like tripartite entanglement is not allowed in holography. In this work, we generalize this holographic signal inequality to mixed states. In a minimal extension, we compute the reflected genuine multi-entropy following \cite{Yuan:2024yfg} and find a class of holographic geometries that violate this minimally extended inequality due to a vanishing Markov gap. We can symmetrize this prescription, where instead of computing the residual information on the given mixed state ρ_ABC, we compute it on its canonical purification. The inequality is restored on the canonically purified state. Finally, we conjecture a new inequality for tripartite holographic states and give supporting evidence.
ER  -