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. Since no pure entanglement can be distilled from them, they are also called bound entangled. In this paper, we present two classes of (2d x 2d)-dimensional PPT entangled states for any d >= 2 which outperform all separable states in metrology significantly. We present strong evidence that our states provide the maximal metrological gain achievable by PPT states for a given system size. When the dimension d goes to infinity, the metrological gain of these states becomes maximal and equals the metrological gain of a pair of maximally entangled qubits. Thus, we argue that our states could be called PPT singlets.

Automated summary

In this paper, two classes of PPT entangled states for any dimension d >= 2 are presented, which outperform all separable states significantly in metrology. It is shown that these states provide the maximal metrological gain achievable by PPT states for a given system size, and reach a maximal metrological gain equal to a pair of maximally entangled qubits as the dimension d goes to infinity. Therefore, these states could be considered as PPT singlets.