Quantum estimation of detection efficiency with no-knowledge quantum feedback

We investigate that no-knowledge measurement-based feedback control is utilized to obtain the estimation precision of the detection efficiency. We show that no-knowledge measurement is the optimal way to estimate the detection efficiency. The higher precision can be achieved for the lower or larger detection efficiency. It is found that no-knowledge feedback can be used to cancel decoherence. No-knowledge feedback with a high detection efficiency can perform well in estimating frequency and detection efficiency parameters simultaneously; simultaneous estimation is better than independent estimation given by the same probes.