Bound Entangled Singlet-Like States for Quantum Metrology

Bipartite entangled quantum states with a positive partial transpose (PPT),i.e., PPT entangled states, are usually considered very weakly entangled. Sinceno pure entanglement can be distilled from them, they are also called boundentangled. In this paper we present two classes of (2d× 2d)-dimensionalPPT entangled states for any d≥ 2 which outperform all separable states inmetrology significantly. We present strong evidence that our states provide themaximal metrological gain achievable by PPT states for a given system size.When the dimension d goes to infinity, the metrological gain of these statesbecomes maximal and equals the metrological gain of a pair of maximallyentangled qubits. Thus, we argue that our states could be called "PPTsinglets."