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On two maximally entangled couples

Felix Huber, Jens Siewert

Abstract

In a seminal article, Higuchi and Sudbery showed that a pure four-qubit state can not be maximally entangled across every bipartition. Such states are now known as absolutely maximally entangled (AME) states. Here we give a series of old and new proofs of the fact that no four-qubit AME state exists. These are based on invariant theory, methods from coding theory, and basic properties from linear algebra such as the Pauli commutation relations.

On two maximally entangled couples

Abstract

In a seminal article, Higuchi and Sudbery showed that a pure four-qubit state can not be maximally entangled across every bipartition. Such states are now known as absolutely maximally entangled (AME) states. Here we give a series of old and new proofs of the fact that no four-qubit AME state exists. These are based on invariant theory, methods from coding theory, and basic properties from linear algebra such as the Pauli commutation relations.

Paper Structure

This paper contains 1 section, 2 theorems, 57 equations.

Table of Contents

  1. Three-qubit GHZ states

Key Result

Lemma 2

All pure three-qubit states with three maximally mixed 1-RDM are local unitary equivalent to the standard GHZ state $(\mathinner{|000\rangle}+ \mathinner{|111\rangle})/\sqrt{2}$.

Theorems & Definitions (12)

  • proof
  • Remark 2
  • Lemma 2
  • proof
  • proof
  • proof
  • proof
  • Remark 3
  • proof
  • Remark 4
  • ...and 2 more