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 nonclassical properties such as genuine multipartite entanglement or violation of Bell inequalities.

• Received 4 June 2019

DOI:https://doi.org/10.1103/PhysRevA.100.032112