Entanglement and quantum combinatorial designs

TL;DR

This paper introduces new quantum combinatorial designs, such as quantum Latin squares and orthogonal arrays, which naturally generate highly entangled multipartite states with potential applications in quantum information processing.

Contribution

It defines quantum combinatorial designs and demonstrates their ability to produce highly entangled multipartite states with high entanglement persistency.

Findings

Existence of infinitely many mutually orthogonal quantum Latin arrangements.

Construction of quantum orthogonal arrays with arbitrarily many columns.

Generated states exhibit high persistency of entanglement.

Abstract

We introduce several classes of quantum combinatorial designs, namely quantum Latin squares, cubes, hypercubes and a notion of orthogonality between them. A further introduced notion, quantum orthogonal arrays, generalizes all previous classes of designs. We show that mutually orthogonal quantum Latin arrangements can be entangled in the same way than quantum states are entangled. Furthermore, we show that such designs naturally define a remarkable class of genuinely multipartite highly entangled states called $k$-uniform, i.e. multipartite pure states such that every reduction to $k$ parties is maximally mixed. We derive infinitely many classes of mutually orthogonal quantum Latin arrangements and quantum orthogonal arrays having an arbitrary large number of columns. The corresponding multipartite $k$-uniform states exhibit a high persistency of entanglement, which makes them ideal candidates to develop multipartite quantum information protocols.