  Tailoring spectral properties of photon pairs is of great importance for
optical quantum information and measurement applications. High-resolution
spectral measurement is a key technique for engineering spectral properties of
photons, making them ideal for various quantum applications. Here we
demonstrate spectral measurements and optimization of frequency-entangled
photon pairs produced via spontaneous parametric downconversion (SPDC),
utilizing frequency-resolved sum-frequency generation (SFG), the reverse
process of SPDC. A joint phase-matching spectrum of a nonlinear crystal around
1580 nm is captured with a 40 pm resolution and a > 40 dB signal-to-noise
ratio, significantly improved compared to traditional frequency-resolved
coincidence measurements. Moreover, our scheme is applicable to collinear
degenerate sources whose characterization is difficult with previously
demonstrated stimulated difference frequency generation (DFG). We also
illustrate that the observed phase-matching function is useful for finding an
optimal pump spectrum to maximize the spectral indistinguishability of SPDC
photons. We expect that our precise spectral characterization technique will be
useful tool for characterizing and tailoring SPDC sources for a wide range of
optical quantum applications
