  High-precision nonlocal temporal correlation identification in the entangled
photon pairs is critical to measure the time offset between remote independent
time scales for many quantum information applications. The first nonlocal
correlation identification was reported in 2009, which extracts the time offset
via the algorithm of iterative fast Fourier transformations (FFTs) and their
inverse. The least identification resolution is restricted by the peak
identification threshold of the algorithm, and thus the time offset calculation
precision is limited. In this paper, an improvement for the identification is
presented both in the resolution and precision via a modified algorithm of
direct cross correlation extraction. A flexible resolution down to 1 ps is
realized, which is only dependent on the Least Significant Bit (LSB) resolution
of the time-tagging device. The attainable precision is shown mainly determined
by the inherent timing jitter of the single photon detectors, the acquired pair
rate and acquisition time, and a sub picosecond precision (0.72 ps) has been
achieved at an acquisition time of 4.5 s. This high-precision nonlocal
measurement realization provides a solid foundation for the field applications
of entanglement-based quantum clock synchronization, ranging and
communications.
