Fig. 1. Flow diagram of the experimental structure. An untrusted coherent state (CS) is divided into two identical and probably impure parts, CS1 for measuring quadrature Q^ and CS2 for quadrature P^. The collected data of one quadrature are chosen as the check quadrature to estimate the conditional min-entropy of the conjugate quadrature of the other state since the dividing process is completely trusted and the distributions of two parts are identical. After two randomness extractors, the secure random bits are obtained. CS, coherent state; OSC, oscilloscope.

Fig. 2. Experimental schematic configuration for mutually testing SDI QRNG. The pink area is a private space that no eavesdropper has access to. The black and blue curves represent the electric and data cables, respectively. The coherent state is generated via a laser and MC. The laser beam is divided into the signal beam and LO via a 98:2 BS. Both the signal beam and the LO are split in half via two 50:50 BSs. Two BHDs are used to measure the quadrature P^ and Q^ of the two coherent states with the phase differences (0 and π/2) between the signal beam and LO, respectively. All data are recorded by an OSC, and the post-processing is achieved via a PC. Laser, Nd:YVO4; MC, mode-cleaner; 98:2, 98:2 beam splitter; 50:50, 50:50 beam splitter; LO, local oscillator; BHD, balanced homodyne detector; HR, mirror with high reflectivity; OSC, oscilloscope; PC, personal computer.

Fig. 3. Red, blue, and black curves show the autocorrelations calculated from the raw bits, the downsampled bits, and the extracted bits, respectively. The three data streams have the same length of 5×107.

Fig. 4. Comparison of the data acquisitions and appropriate time sequences of mutually testing and randomly toggling manners. The red and blue points represent the measured data of quadratures P^ and Q^, respectively. (a), (b) The data acquisitions on the conjugate quadratures P^ and Q^ in mutually testing manner. (c) The data acquisitions for raw random numbers on the quadratures Q^ in randomly toggling manner. The data of quadratures P^ are used to estimate the randomness of quadratures Q^ and never generate random numbers. (d) Time sequences. Black and red curves represent the time sequences for randomly measuring electronic noise and check quadrature, respectively.

Fig. 5. Schematic of the balanced homodyne detection. The difference current is converted into an amplified voltage signal by a transimpedance amplifier.