## 3 Experimental Setup and Results
The continuous LO beam was used to measure the noise variance of a coherent state, and the dependence of measured extra noise of the output state at usual analysis frequency range (1.0 MHz to 6.0 MHz) on the transmission distance of fiber is given in Figure 3. The green rhombuses, red triangles, black rectangles, and blue dots correspond to measured noise variance of a coherent state when the powers of LO beam in BHD2 are 0.2 mW, 0.5 mW, 1.0 mW and 2.1 mW, respectively. The traces in each color are the fitting results with the corresponding experimental data and these results showed that \(\varepsilon=0.16\) m\({}^{-1}\cdot\)W\({}^{-1}\) at this frequency range according to the Equation (3). Figure 3: The dependence of the measured noise variance of a coherent state on the transmission distance in the fiber. The green, red, black, and blue traces correspond to the powers of LO beam in BHD2 of 0.2 mW, 0.5 mW, 1.0 mW and 2.1 mW, respectively. Figure 2: Schematic diagram of the experimental device. OPA: optical parametric amplifier. PPKTP: periodically poled KTiOPO\({}_{4}\). AM: amplitude modulator. HWP1-3: half wavelength plate. ISO: isolator. FC: fiber coupler. PC: polarization controller. OPD: optical path delay of the LO beam. BHD1-2: balanced homodyne detection. BHD1 was used to measure the noise variance of the quantum state before the fiber. BHD2 was used to measure the noise variance of the quantum state output from the fiber. In order to know the influence of GAWBS on the transmission of nonclassical state, the dependencies of measured noise variance of the signal beam with on the transmission distance are given in Figure 4a. The red and blue traces correspond to the measured noise variances of squeezed state and coherent state with a continuous LO beam, respectively. Here, the power of LO beam in BHD2 is kept at 1.0 mW. When the transmitted state was a \(-4.0\) dB squeezed state, the calculated result shows that the squeezing vanished when the transmission distance was about 2.6 km. Thus the continuous LO beam must be changed to pulsed LO beam to eliminate the influence of GAWBS as the previous theoretical analysis. The second scheme as shown in Figure 1b was chosen in our experiment. The calculated result, which is given as the orange trace in Figure 4, shows that the squeezing property can be kept even when the transmission distance is very long. The dot, triangle and square are the corresponding measured results with different transmission distances. When the transmission distance was 19.2 km and the total transmission efficiency \(\eta\) was 18%, the measured noise variance of squeezed state was still 0.42 dB below the corresponding QNL. The result shows that the transmission distances can be greatly improved if the pulsed LO beam is used in the BHD system. In order to verify the feasibility of our protocol, the dependence of the noise variances of coherent state and squeezed state on the different power of LO beams in BHD2 are given in Figure 4b when the fiber length was 5.0 km. It is obvious that when the LO beam was pulsed, the squeezing level of the transferred squeezed state still remained at \(-1.6\) dB, which indicates that the influence of GAWBS noise can be completely eliminated with this transmission scheme. At this time, the transferring of the signal beam is only affected by the transmission loss in the fiber.