On circulant states with positive partial transpose

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.

15 pages; minor corrections

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• Generalized Circulant Densities and a Sufficient Condition for Separability
• Entangled symmetric states and copositive matrices
• Bell diagonal states with maximal abelian symmetry
• Bipartite bound entanglement in continuous variables through deGaussification
• Entanglement witnesses for $d\otimes d$ systems and new classes of entangled qudit states
• A bipartite separable ball and its applications
• Bounds on bipartite entanglement from fixed marginals
• On a characterization of PPT states
• On the symmetry of the seminal Horodecki state
• On correlations and mutual entropy in quantum composed systems
• On classical and quantum liftings
• Nongeneric positive partial transpose states of rank five in $3\times 3$ dimensions
• Local numerical range for a class of $2\otimes d$ hermitian operators
• Controlling nonlocality of bipartite qubit states via quantum channels