Bound entangled "singlets" for quantum metrology.

Bipartite entangled quantum states with a positive partial transpose (PPT). i.e., PPT entangled states, are usually considered to be very weakly entangled. Since no pure entanglement can be distilled from them, they are also called bound entangled. In this paper we present two classes of ($2d\times 2d$)-dimensional PPT entangled states for any $d\ge 2$ which outperform all separable states in metrology significantly. The metrological gain of these PPT states becomes maximal corresponding to a pair of maximally entangled qubits when dimension $d$ goes to infinity. We have strong evidence that our states have maximal quantum Fisher information among PPT entangled states with a given dimension. Thus, they could be called "PPT singlets."