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On Non-Existence of Stabilizer Absolutely Maximally Entangled States in Even Local Dimensions

Jakub Wójcik, Owidiusz Makuta, Wojciech Bruzda, Remigiusz Augusiak

Abstract

We demonstrate that absolutely maximally entangled (AME) states consisting of $N=4k$ qudits with $k\in\mathbb{N}_+$, each of even local dimension, cannot be realized as graph states. This result imposes strong constraints on AME states in composite local dimensions and characterizes the limitations of graph-state constructions for highly entangled multipartite quantum systems. In particular, this study provides an independent solution of the recently discussed case of the AME state of four quhexes and clarifies its characterization within the stabilizer formalism, complementing the results of Cha [arXiv:2603.13442].

On Non-Existence of Stabilizer Absolutely Maximally Entangled States in Even Local Dimensions

Abstract

We demonstrate that absolutely maximally entangled (AME) states consisting of qudits with , each of even local dimension, cannot be realized as graph states. This result imposes strong constraints on AME states in composite local dimensions and characterizes the limitations of graph-state constructions for highly entangled multipartite quantum systems. In particular, this study provides an independent solution of the recently discussed case of the AME state of four quhexes and clarifies its characterization within the stabilizer formalism, complementing the results of Cha [arXiv:2603.13442].
Paper Structure (5 sections, 3 theorems, 19 equations)

This paper contains 5 sections, 3 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Result
  4. Summary
  5. Acknowledgments

Key Result

Lemma 1

A graph state $\ket{G}$ stabilized by $\mathbb{S}$ is AME iff

Theorems & Definitions (6)

  • Lemma 1
  • proof
  • proof
  • Theorem 1
  • proof
  • Corollary 1