Purity and construction of arbitrary dimensional $k$-uniform mixed states

TL;DR

This paper introduces new methods to construct high-purity, arbitrary-dimensional k-uniform mixed states using orthogonal arrays, expanding the known classes of such states with potential applications in quantum information.

Contribution

The paper develops novel construction techniques for k-uniform mixed states with maximal purity, utilizing orthogonal array partitions, and demonstrates the generation of infinite higher-dimensional states.

Findings

Constructed new k-uniform mixed states with maximal purity.

Derived an infinite series of higher-dimensional k-uniform states.

Established a link between orthogonal arrays and quantum state construction.

Abstract

k-uniform mixed states are a significant class of states characterized by all k-party reduced states being maximally mixed. Novel methodologies are constructed for constructing k-uniform mixed states with the highest possible purity. By using the orthogonal partition of orthogonal arrays, a series of new $k$-uniform mixed states is derived. Consequently, an infinite number of higher-dimensional k-uniform mixed states, including those with highest purity, can be generated.