# $k$-uniform mixed states

## TL;DR

This paper explores the maximum purity of k-uniform mixed states in N-party quantum systems, proposing explicit construction methods and demonstrating their non-classical properties like entanglement and Bell inequality violations.

## Contribution

It introduces a scheme to explicitly construct k-uniform states using N-qubit Pauli matrices and provides examples linking these states to orthogonal arrays.

## Key findings

- Constructed explicit examples of k-uniform states.
- Demonstrated these states exhibit genuine multipartite entanglement.
- Showed some states violate Bell inequalities.

## Abstract

We investigate the maximum purity that can be achieved by k-uniform mixed states of N parties. Such N-party states have the property that all their k-party reduced states are maximally mixed. A scheme to construct explicitly k-uniform states using a set of specific N-qubit Pauli matrices is proposed. We provide several different examples of such states and demonstrate that in some cases the state corresponds to a particular orthogonal array. The obtained states, despite being mixed, reveal strong non-classical properties such as genuine multipartite entanglement or violation of Bell inequalities.