Using the coincidence-count (CC) measurement of the generated frequency-entangled twin-photons beam (TWB) via the process of type-I spontaneous parametric-down conversion (SPDC) in BBO nonlinear crystal (NLC), we have precisely measured the transmittance of very diluted Rabbit-and Human-DNA, Methylene-Blue (MB), as a disinfectant, and thin-film multilayer at near IR wavelength 810nm with an accuracy in order of %0.01 due to the quantum correlation, while accuracy of classical-like measurement, single-count (SC), is in order of %0.1 in our setup. Moreover, using quantum measurement of the transmittance, the different types of DNA with the same concentration, and also very diluted (in order of pg/𝜇l) different concentrations of DNA and MB solutions are distinguished and detected with high-reliability. Interestingly, in case of Human-DNA samples in contrast to our classical-like measurement we could precisely detect and distinguish two very diluted concentrations 0.01ng/𝜇l and 0.1ng/𝜇l with high reliability while commercial standard spectrometer device of our DNA-manufacturer never could detect and distinguish them. Surprisingly, measurement on the thin-film multilayer illustrates that the introduced method in this work might be performed to cancer/brain tissues or Stem cells for cancer therapy, and may hopefully open a pave and platform for non-invasive quantum diagnosis in future.