Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays

TL;DR

This paper develops a new method to construct highly entangled quantum states in heterogeneous systems using irredundant mixed orthogonal arrays, solving open problems and providing explicit examples for various system configurations.

Contribution

It extends orthogonal array methods to heterogeneous quantum systems and constructs infinite classes of k-uniform states, addressing open questions in quantum entanglement theory.

Findings

Constructed infinite classes of k-uniform states for heterogeneous systems.

Extended methods from homogeneous to heterogeneous quantum systems.

Proved non-existence of certain irredundant mixed orthogonal arrays.

Abstract

Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays (OAs) to heterogeneous multipartite systems with different individual levels. The second is the existence of $k$-uniform states in heterogeneous quantum systems. We present explicit constructions of two and three-uniform states for arbitrary heterogeneous multipartite systems with coprime individual levels, and characterize the entangled states in heterogeneous systems consisting of subsystems with nonprime power dimensions as well. Moreover, we obtain infinite classes of $k$-uniform states for heterogeneous multipartite systems for any $k\geq2$. The non-existence of a class of IrMOAs is also proved.