Enhancing the precision of multi-parameter estimation for two-level open quantum system by mixed control

The article delves into the advancements in quantum metrology, focusing on the simultaneous estimation of multiple parameters in open quantum systems. Traditional measurement techniques are limited by the shot-noise and standard quantum limits, but quantum mechanisms like squeezing and entanglement offer a path to surpass these bounds. The research highlights the importance of suitable probe states, measurement schemes, and controls to enhance precision. The paper introduces a mixed control scheme that combines adaptive Markov feedback control and additional adaptive control to improve the precision limit of multi-parameter estimation. The authors analyze three types of feedback operators and demonstrate that the mixed control scheme can significantly enhance the estimation precision, particularly when the decoherence parameter is relatively large. The study also compares the mixed control scheme with the GRAPE method, showing that the proposed scheme outperforms in improving estimation precision. The findings offer promising avenues for future research in complex multi-parameter estimation problems and time-varying signals.