This paper analyzed the zero-point displacement uncertainty determined by Heisenberg uncertainty principle in the silicon cantilever nano-resonators with the thicknesses of 12 nm and 38.5 nm. The analysis results show that the zero-point displacement uncertainty is inversely proportional to the thickness and width of the cantilever and proportional to the length of the cantilever, and the zero-point displacement uncertainty of the silicon cantilever nano-resonator with the thickness of 12 nm is 4.1×10-3 nm. Combining the parametric pumping quantum squeezing technique, the relationships between the quantum-squeezing factors of the silicon cantilever nano-resonators with different thicknesses and their structure dimensions, temperatures, pumping voltages were analyzed. The analysis results show that the quantum-squeezing factor is proportional to the temperature, and inversely proportional to the pumping voltage. When the temperature is 0.01 K and the pumping voltage equals 4 V, the quantum noise of the silicon cantilever nano-resonator with the thickness of 12 nm is reduced by 26.56 dB. The analysis results promote the improvement of the measurement accuracy of the ultra-thin cantilever nano-resonators under the influence of the quantum noises observably.