## 4 Conclusions  
We proposed and experimentally realized a QRNG scheme utilizing quantum noise from phase fluctuation of laser diode with a novel structure. Optical signals from two laser diodes with very close center wavelength interfere at a beam splitter before detected by AC coupling photo-detectors. Electric signals from two detectors did frequency mixing with a mixer. After analyzing the frequency components, we pointed out there are three dominating frequency terms in the noise: difference of the center wavelength of laser, phase fluctuation of laser, and fiber jitter of the system. Due to the different frequency range between these components, we found it possible to substantially eliminate the unexpected terms by a well selected band-pass filter, before extracting randomness with the phase noise term. We use two conventional post-processing methods, the \(m\)-least significant bit method (\(m\)-LSB) and universal (Toeplitz) hashing method, to distill randomness from electric signal, and realize a generation rate of 600 Mb/s on hardware, which is six times higher than the sampling rate. Our scheme has three major merits. Firstly, the structure of our scheme is delay-line free, which means the space for delay-line in practical system could be removed. Secondly, the requirement for laser diode is not so strict. One only need to make sure the center wavelength of lasers are close enough, and work with a power stabilization module, instead of a possible frequency stabilization module. Thirdly, the post-processing methods, either \(m\)-LSB or universal hashing method, can be realized on hardware in real-time. These merits make our scheme highly potential as a compact QRNG system. We should admit that the generation rate in our scheme is relatively low in contrast to current schemes. However, this is due to building our scheme in a very conservative way and this work is just a demonstration. The bandwidth of photo-detectors and the sampling rate are both set at 100 MHz, where devices used in major schemes of phase noise are one or two orders of magnitude higher than this value. Since the generation rate is mainly limited by the detectors, it still have huge space to improve. In fact, our colleagues have realized balanced detectors with bandwidth over 1 GHz [55]. By utilizing this technique, the generation rate of our scheme is highly potential to be increased to 6 Gbps, which is the level the other QRNG scheme based on vacuum fluctuation proposed before [44]. Furthermore, the corresponding post-processing method can also be more efficient, including carefully setting the driven current of laser diode to achieve a higher quantum-to-classical noise ratio, which could lead to an even tighter upper bound of min-entropy in Toeplitz hashing method. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Statistical Test** & \(p\)**-Value** & **Proportion** & **Result** \\ \hline Frequency & 0.372076 & 597 & Success \\ Block Frequency & 0.292462 & 596 & Success \\ Cumulative Sums & 0.045724[KS] & 590 & Success \\ Runs & 0.294970 & 593 & Success \\ Longest Run & 0.940051 & 592 & Success \\ Rank & 0.316426 & 595 & Success \\ FFT & 0.959554 & 590 & Success \\ Non-overlapping & 0.743782[KS] & 595 & Success \\ Overlapping & 0.065969 & 596 & Success \\ Universal & 0.494772 & 598 & Success \\ Approx. Entropy & 0.908376 & 596 & Success \\ Excursions & 0.558001[KS] & 593 & Success \\ Excursions Var. & 0.032325[KS] & 590 & Success \\ Serial & 0.225053[KS] & 592 & Success \\ Complexity & 0.869431 & 595 & Success \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The result of the NIST-STS test after post-processing. The NIST-STS includes 15 terms and respective test results, each with a \(p\)-value. For the sub-tests with multiple \(p\)-values, a Kolmogorov-Smirnov (KS) test is performed to obtain final \(p\)-value. It is considered successful for certain sub-test if the final \(p\)-value is between \([0.01,0.99]\) and the success proportion is between \([0.9778,1]\) (significance level \(\alpha=0.01\)).