We construct a large class of quantum $d\otimes d$ 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 why 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.

• Received 14 June 2007

DOI:https://doi.org/10.1103/PhysRevA.76.032308