Quantum entanglement and the Bell Matrix

TL;DR

This paper introduces a new class of maximally entangled states generated by a high-dimensional generalization of the CNOT gate, with simple algebraic structure and broad applicability across dimensions.

Contribution

It proposes a novel high-dimensional entangling operator and provides new conditions for achieving global and maximal entanglement.

Findings

The entangling operator produces maximally entangled states with simple algebraic form.

The method applies to any dimension, demonstrating its generality.

New sufficient conditions for global and maximal entanglement are established.

Abstract

We present a class of maximally entangled states generated by a high-dimensional generalisation of the \textsc{cnot} gate. The advantage of our approach is the simple algebraic structure of both entangling operator and resulting entangled states. In order to show that the method can be applied to any dimension, we introduce new sufficient conditions for global and maximal entanglement with respect to Meyer and Wallach's measure.