  Entanglement is a fundamental resource of various optical
quantum-information-processing (QIP) applications. Towards high-speed QIP
system, entanglement should be encoded in short wavepackets. We report
real-time observation of ultrafast optical Einstein-Podolsky-Rosen (EPR)
correlation at a picosecond timescale in a continuous-wave (CW) system. Optical
phase-sensitive amplification using 6-THz-bandwidth
waveguide-optical-parametric amplifier enhances the effective efficiency of
70-GHz-bandwidth homodyne detectors, mainly used in 5th-generation
telecommunication, enabling its use in real-time quantum-state measurement.
While power measurement using frequency scanning, i.e., optical spectrum
analyzer, is not performed in real-time, our observation is demonstrated
through real-time amplitude measurement and can be directly employed in QIP
applications. Observed EPR states show quantum correlation of 4.5 dB below
shotnoise level encoded in wavepackets with 40-ps period, equivalent to 25-GHz
repetition -- ${10^3}$ times faster than previous entanglement observation in
CW system. The quantum correlation of 4.5 dB is already sufficient for several
QIP applications, and our system can be readily extended to large-scale
entanglement. Moreover, our scheme has high compatibility with optical
communication technology such as wavelength-division multiplexing, and
femtosecond-timescale observation is also feasible. Our demonstration is
paradigm shift in accelerating accessible quantum correlation, the foundational
resource of all quantum applications, from the nanosecond to picosecond
timescale, enabling ultra-fast optical QIP.
