3-Uniform states and orthogonal arrays

TL;DR

This paper explores the existence of 3-uniform quantum states in N-qubits, establishing their presence for N=11 to 15, and links combinatorial orthogonal arrays to quantum state properties.

Contribution

It demonstrates the existence of 3-uniform states for N=11 to 15 qubits, advancing understanding of quantum state structures and their combinatorial connections.

Findings

3-uniform states exist for N=11 to 15 qubits

Established a link between orthogonal arrays and quantum states

Extended previous theoretical results on uniform states

Abstract

In a recent paper (Phys. Rev. A 90, 022316 (2014) ), Goyeneche et al. established a link between the combinatorial notion of orthogonal arrays and k-uniform states and present open issue. (B) Find for what N there are 3-uniform states of N-qubits. In this paper, we demonstrate the existence of 3-uniform states of N-qubits for N=11,..,15".