Quantum metrology timing limits of biphoton frequency comb

Biphoton frequency comb (BFC), which encompasses multiple discrete frequency modes and represents high-dimensional frequency entanglement, is crucial in quantum information processing due to its high information capacity and error resilience. It also holds significant potential for enhancing timing precision in quantum metrology. Here, we examine quantum metrology timing limits using the BFC as a probe state and derive a quantum Cramér-Rao bound (QCRB) that depends on the mode number, mode spacing, frequency detuning, and single-mode bandwidth. Our results coincide with previous findings that considered only the latter two factors. Under ideal conditions (zero loss and perfect visibility), this bound can be saturated by both spectrally non-resolved Hong-Ou-Mandel (HOM) interferometry at zero delay and spectrally resolved HOM interferometry at arbitrary delays. In practical scenarios, the Fisher information is below the QCRB but can approach its maximum by increasing the mode number and mode spacing for a fixed delay point, suggesting an optimal strategy for improving the precision of HOM-based sensing in practice. Furthermore, compared to spectrally non-resolved measurement, spectrally resolved measurement is a superior strategy due to its higher Fisher information, shorter measurement times, and ambiguity-free dynamic range.