Quantum microwave photonics (QMWP) is an innovative approach that combines energy–time entangled biphoton sources as the optical carrier with time-correlated single-photon detection for high-speed radio frequency (RF) signal recovery. This groundbreaking method offers unique advantages, such as nonlocal RF signal encoding and robust resistance to dispersion-induced frequency fading. We explore the versatility of processing the quantum microwave photonic signal by utilizing coincidence window selection on the biphoton coincidence distribution. The demonstration includes finely tunable RF phase shifting, flexible multitap transversal filtering (with up to 14 taps), and photonically implemented RF mixing, leveraging the nonlocal RF mapping characteristic of QMWP. These accomplishments significantly enhance the capability of microwave photonic systems in processing ultraweak signals, opening up new possibilities for various applications.