The conditions for the generation and detection of quantum-correlated pairs of optical and terahertz photons in the process of strongly frequency-nondegenerate parametric down-conversion of light are investigated. An approach based on increasing the frequency of the optical pump is proposed, whereby the power of a weak flux of terahertz idler photons can be measured for a wide range of parametric gain coefficients, down to the onset of the spontaneous down-conversion regime, using the same terahertz detector with a limited dynamic range. It is shown experimentally that the doubling of the frequency of pulsed laser pump leads to a 5-fold reduction in the lowest value of parametric gain that is still sufficient for detecting terahertz idler photons with a cooled hot-electron bolometer.