On circulant states with positive partial transpose

TL;DR

This paper introduces a broad class of circulant quantum states with positive partial transpose, revealing their cyclic structure and sharing properties under partial transposition, thus unifying known examples and generating new PPT states.

Contribution

The authors develop a novel construction of circulant states with PPT property, expanding the family of known quantum states with positive partial transpose.

Findings

Includes many known PPT states as special cases

Creates a large family of new PPT states

Shows partial transposition preserves circulant structure

Abstract

We construct a large class of quantum "d x d" states which are positive under partial transposition (so called PPT states). The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic circular structure - that is way we call them circulant states. It turns out that partial transposition maps any such decomposition into another one and hence both original density matrix and its partially transposed partner share similar cyclic properties. This class contains many well known examples of PPT states from the literature and gives rise to a huge family of completely new states.