Generalized Criterion of Maximally Multi-Qubit Entanglement

TL;DR

This paper introduces a new generalized criterion for identifying maximally multi-qubit entangled states across various qubit systems, discovering new states and challenging previous assumptions about their existence.

Contribution

The paper proposes a novel criterion for maximally entangled multi-qubit states and identifies new maximally entangled states, including a previously unknown eight-qubit state.

Findings

New criterion for maximally entangled states across multiple qubit systems

Discovery of a new genuine eight-qubit maximally entangled state

Reevaluation of the existence of MMES in 4, 7, and 8 qubits systems

Abstract

We first present a generalized criterion for maximally entangled states of 2, 3, 4, 5, 6, 8 and in theory to arbitrary-number qubits. By this criterion, some known highly entangled multi-qubit states are examined and a new genuine eight-qubit maximally entangle state is obtained. For the 4, 7 and 8 qubits system in which no maximally multi-qubit entangled states (MMES) is thought to exist before, we find that the proved and most suspected MMESes, are not completely mixed in subsystem with a critical-number qubits, below which the subsystems are all completely mixed. We believe that the new criterion and MMES can play important role in quantum information technology, such as the teleportation and dense coding.