Exploring maximally multipartite entanglement of even n qubits with N-tangle

TL;DR

This paper investigates the properties of maximally multipartite entangled states (MMES) in even qubit systems using n-tangle, revealing specific patterns and limitations for different qubit counts and proposing a conjecture for larger systems.

Contribution

It introduces a necessary condition for MMES based on n-tangle values and proposes a conjecture about the pattern of n-tangle in larger even-qubit systems.

Findings

n-tangle equals zero for 4- and 8-qubit MMES

n-tangle equals one for 2- and 6-qubit MMES

Theoretical limitations for 10- and 12-qubit MMES

Abstract

A necessary condition of the maximally multipartite entangled states (MMES) is given via n-tangle. The condition shows that the n-tangle equal zero for the four-, and eight-qubit of MMESs and the n-tangle equal 1 for two- and six- qubits of MMESs. Furthermore,we give the theoretical limitation for maximally ten-qubit and twelve-qubit entangled states. We conjecture that 4n-qubit states of MMES should have n-tangle equal zero and 4n+2-qubit states of MMES should have n-tangle equal one.