Chaotic Time-delay Signature Suppression And Entropy Enhancement Based On Quantum Noise

With the rapid development of information technology,the modern communication technology based on the communication network has penetrated into people's production and life.Ensurig high-speed and safe transmission of information has become an important goal of various countries in the communication field.Chaotic light has been widely used in secure communication and physical random number generation due to its non-linear dynamic characteristics such as noise-like randomness and sensitivity to initial value conditions.As a typical chaotic dynamic system,the semiconductor laser with external optical feedback can output high-dimensional chaotic signals,providing a good platform for the study of nonlinear effects and complex photon dynamics.However,the external optical feedback gives rise to a periodic time-delay signature(TDS).The TDS could expose the information related to the length of the feedback external cavity,posing a threat to the security of secure communication.Meanwhile,TDS makes the chaotic signals appear weak periodicity in the time domain,reducing the randomness and entropy of the chaotic signals and affecting the quality of physical random number generation.Therefore,it is of great significance to study TDS suppression and entropy enhancement,obtaining high-quality chaotic laser signals.Up to now,many schemes have been reported to suppress the TDS of chaotic laser,including external parameter-condition tuning and post-processing.The above methods are also to extract the randomness from chaotic dynamics.Random fluctuation of chaotic light field originates from the intrinsic quantum shot noise.There are many kinds of initial noises in the real chaotic physical system.Among them,the quantum noise provides a stochastic initial value for the chaotic system,and the randomness of the quantum noise can be rapidly and nonlinearly amplified by the chaotic system to generate random fluctuation.While the nonlinear amplification of intrinsic quantum noise by the chaotic system is entirely distinct from the noise-like fluctuation induced by deterministic chaos.Therefore,it has become one of the urgent problems to reveal the origin of random effect and the influence of quantum noise on the underlying dynamics of chaotic laser.Quantum noise is a kind of white noise with infinite bandwidth,and the quantum modes of different frequencies are independent.At present,the quantum noise can be extracted by the balanced homodyne technology with high quantum efficiency.And the parallel quantum random number generation with a real-time generation rate of 8.25Gbit/s based on the quantum noise has been realized experimentally.The randomness and complexity of chaotic laser are the basis of its information security and cryptographic applications.Nowadays,many kinds of entropy have been proposed to quantify the randomness of chaotic laser,such as Shannon entropy,Kolmogorov-Sinai entropy and Permutation entropy.In the process of quantifying the entropy value of chaotic laser,these entropy forms still face some difficulties,such as accurately quantify entropy evolution of chaotic laser and evaluate whether the chaotic dynamics is noise-dominated or not.Entropy content is the quantitative standard of physical randomness,and the entropy growth describes the generation and evolution of the randomness of the system.The higher the entropy content of the entropy source,the higher the security and robustness of the random code generator,and the larger the proportion of true randomness that can be extracted from the original data.Therefore,how to quantify the entropy value of the physical entropy source in real time and effectively enhance the entropy content of the entropy source is also one of the urgent problems to be solved.In view of the above problems,the main contents of this study are as follows:1)Here we numerically and experimentally demonstrate a technique to effectively suppress the TDS of chaotic lasers using quantum noise.In theory,the Lang-Kobayashi rate equation with Gaussian white noise is constructed to simulate the dynamics characteristics of chaotic laser after injecting quantum noise.In experiment,quantum noise from quadrature fluctuations of vacuum state is prepared through balanced homodyne measurement.And the TDS is quantified using the autocorrelation function and normalized permutation entropy at the feedback delay time.The results show that compared to the original chaos,the TDS of this quantum-noise improved chaos is suppressed up to 94%and the bandwidth suppression ratio of quantum noise to chaotic laser is 1:25.It indicates that narrow bandwidth quantum noise substantially suppresses the TDS of wide bandwidth chaotic laser.The effects of strength and bandwidth of quantum noise on chaotic TDS suppression are investigated numerically and experimentally.The experimental results agree well with the theoretical results.Increasing the bandwidth and strength of quantum noise can significantly suppress chaotic TDS.And the probability statistical distribution of chaotic intensity is significantly improved and fits well with Gaussian random distribution,that is,the randomness of chaotic laser signals is improved.It reveals that the randomness of chaotic laser comes from random quantum noise.2)A chaotic laser prepared by a semiconductor laser with external optical feedback is used as an entropy source.The effects of different intensities and bandwidths of quantum noise on the entropy enhancement of the chaotic laser are studied numerically and experimentally.The mean value of permutation entropy at the feedback delay time?_ext,?_ext/2,?_ext/3 is used for quantifying the complexity of the chaotic signal.The permutation entropy growth G_dbetween the adjacent embedding dimension is used to evaluate whether the chaotic dynamics is noise-dominated or not.The entropy growth of chaotic laser versus quantum noise strength for different quantum noise bandwidths:100MHz,300MHz,and 500MHz.The results demonstrate that narrow-bandwidth quantum noise substantially enhances the entropy of wide-bandwidth chaotic laser,and the mean entropy or whole complexity of the 3.8GHz bandwidth chaotic laser is increased to 0.998 in the case of quantum noise injection with an strength of 15d Bm and a bandwidth of 100MHz.Moreover,the quantum noise bandwidth,which is needed to enhance the entropy of chaotic laser to the maximum,decreases as the strength of quantum noise increases.In addition,as the strength of quantum noise increases,the entropy growth G_dis greater than the noise-dominated threshold G_d^{Nt h r}.And G_dincreases monotonically as the embedding dimension d increases.The results show that the chaotic dynamics process is dominated by random noise,that is,the chaotic laser output of random noise domination and entropy enhancement is obtained.The improved chaotic laser has potential applications in random number generation and secure communication.