Activating Hidden Metrological Usefulness

We consider bipartite entangled states that cannot outperform separable states in any linear interferometer. Then, we show that these states can still be more useful metrologically than separable states if several copies of the state are provided or an ancilla is added to the quantum system. We present a general method to find the local Hamiltonian for which a given quantum state performs the best compared to separable states. We obtain analytically the optimal Hamiltonian for some quantum states with a high symmetry. We show that all bipartite entangled pure states outperform separable states in metrology. Some potential applications of the results are also suggested.

Figure 1

(a) An ancilla (“$a$”) is added to bipartite state ${\varrho }_{AB}$. (b) An additional copy or a different state is added to the state. In both cases, a new bipartite state is obtained, where the two parties are separated by a dashed line.