Ultimate precision limit of noise sensing and dark matter search

The nature of dark matter is unknown and calls for a systematical search. For axion dark matter, such a search relies on finding feeble random noise arising from the weak coupling between dark matter and microwave haloscopes. We model such process as a quantum channel and derive the fundamental precision limit of noise sensing. An entanglement-assisted strategy based on two-mode squeezed vacuum is thereby demonstrated optimal, while the optimality of a single-mode squeezed vacuum is found limited to the lossless case. We propose a 'nulling' measurement (squeezing and photon counting) to achieve the optimal performances. In terms of the scan rate, single-mode squeezing underperforms the vacuum limit of photon counting even with 20-decibel squeezing; while the two-mode squeezed vacuum provides large and close-to-optimum advantage over vacuum limit. Our results highlight the necessity of entanglement assistance and microwave photon counting in dark matter search, while more exotic quantum resources are not required.