Quantum metrology with general measurements

The field of quantum metrology seeks to develop quantum protocols to enhance the precision of measurements and it is one of the pillars of quantum science and technology. The general tools and bounds of quantum metrology assume perfect detection. However, the detection in most quantum experimental platforms is noisy and imperfect. We fill this gap and develop a theory that takes into account general measurements . We generalize the precision bounds to account for arbitrary detection channels. We find the general form of the precision bounds and of the optimal control for pure states. We then consider quantum states in a multi-partite system and study the impact of detection noise on quantum enhancement in sensitivity. Interestingly, the achievable sensitivity depends crucially on the allowed control operations. For local optimal control, the detection noise severely degrades the sensitivity and limits any quantum enhancement to a constant factor. On the other hand, with optimal global control the detection noise can be completely removed and the noiseless sensitivity bounds can be retrieved for a generic class of quantum states (including all pure states and symmetric states).

Based on https://www.nature.com/articles/s41467-022-33563-8, https://arxiv.org/abs/2210.11393