  Timing and positioning measurements are key requisites for essential quantum
network operations such as Bell state measurement. Conventional time-of-flight
measurements using single-photon detectors are often limited by detection
timing jitter. In this work, we demonstrate a nonlocal scheme to measure
changes in relative link latencies with subpicosecond resolution by using tight
timing correlation of broadband time-energy entangled photons. Our sensing
scheme relies on spectral interference achieved via phase modulation, followed
by filtering and biphoton coincidence measurements, and is resilient to
microsecond-scale mismatch between the optical link traversed by the biphotons.
Our experiments demonstrate a precision of +/-0.04 ps in measurements of
nonlocal delay changes and +/-0.7{\deg} in measurements of radio-frequency
phase changes. Furthermore, we complement our technique with time-tag
information from single-photon detectors in the same setup to present
unambiguous sensing of delay changes. The proposed technique can be implemented
using off-the-shelf telecom equipment thus rendering it adaptable to practical
quantum network infrastructure.
