# Entanglement in Higher-Radix Quantum Systems

## TL;DR

This paper explores entanglement in higher-radix quantum systems, introducing partial entanglement, differentiating it from maximal entanglement, and developing circuits to generate these states, expanding quantum information processing capabilities.

## Contribution

It introduces the concept of partial entanglement in higher-radix systems and develops circuits for generating both partial and maximal entangled states.

## Key findings

- Defined partial entanglement for radix- greater than two
- Developed higher-radix maximal entanglement generator circuits
- Demonstrated entanglement generation in radix-4 qudits

## Abstract

Entanglement is an important phenomenon that enables quantum information processing algorithms and quantum communications protocols. Although entangled quantum states are often described in radix-2, higher-radix qudits can become entangled as well. In this work, we both introduce partial entanglement, a concept that does not exist for radix-2 quantum systems, and differentiate between partial and maximal entanglement within non-binary quantum information processing systems. We also develop and present higher-radix maximal entanglement generator circuits that are analogous to the well-known Bell state generator for binary quantum systems. Because higher-dimensioned qudits can be subjected to entangling processes that result in either partially or maximally entangled states, we demonstrate how higher-radix qudit circuits can be composed to generate these varying degrees of partial quantum entanglement. Theoretical results are provided for the general case where the radix is greater than two, and specific results based on a pair of radix-4 qudits are described.