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A stabilizer $\mathrm{AME}(4,6)$ state does not exist

Hyunho Cha

Abstract

We prove the non-existence of stabilizer absolutely maximally entangled states for systems of four six-dimensional qudits.

A stabilizer $\mathrm{AME}(4,6)$ state does not exist

Abstract

We prove the non-existence of stabilizer absolutely maximally entangled states for systems of four six-dimensional qudits.
Paper Structure (4 sections, 5 theorems, 14 equations)

This paper contains 4 sections, 5 theorems, 14 equations.

Table of Contents

  1. Preliminaries
  2. Basic definitions
  3. Known results
  4. Main result

Key Result

Theorem 1

For every integer $n\ge 1$, every stabilizer state $|\Phi\rangle\in (\mathbb{C}^6)^{\otimes n}$ is locally unitarily equivalent to a tensor product of a qubit stabilizer state and a qutrit stabilizer state. More explicitly, there exists a unitary such that for every stabilizer state $|\Phi\rangle\in (\mathbb{C}^6)^{\otimes n}$ there exist stabilizer states with where the right-hand side is view

Theorems & Definitions (7)

  • Definition 1: Absolutely maximally entangled state on four parties
  • Theorem 1: looi2011tripartite, Corollary 5
  • Theorem 2: higuchi2000entangled, Theorem 1
  • Theorem 3
  • proof
  • Theorem 4
  • Corollary 1