Multipartite circulant states with positive partial transposes

TL;DR

This paper introduces a broad class of multipartite qudit states with positive partial transposes, generalizing previous bipartite circulant states and encompassing many known quantum states while also creating many new ones.

Contribution

The authors develop a novel construction method for multipartite circulant states with positive partial transposes, extending prior bipartite models to multipartite systems.

Findings

Includes many well-known quantum states as special cases

Generates a large family of new quantum states

Provides a unifying framework for circulant states

Abstract

We construct a large class of multipartite qudit states which are positive under the family of partial transpositions. The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic circular structure and hence generalizes a class of bipartite circulant states proposed recently by the authors. This class contains many well known examples of multipartite quantum states from the literature and gives rise to a huge family of completely new states.