无法预测的自然界真随机数:一种高效量子随机发生器的实验验证

随机数是科学、工程和经济领域中的一项重要资源。从最初的彩票摇奖,到计算机指令开发,再到互联网中的各种密钥,随机数的质量或真伪,直接决定了一套系统的基石是否稳固。

大多数计算机中都采用基于某种确定性数学算法和随机种子的方法来产生具有随机统计分布的数据,但原则上这些随机数可能被预测,故称作伪随机数。

真随机数可以通过某些不可预测的物理事件产生,其随机性可以由物理过程中的内在特性确保。量子非局域关联是量子信息理论众多重要应用所关注的焦点,已广泛应用于量子密钥分配、纠缠认证和随机性生成等。

量子随机数发生器就是建立在量子理论的内禀随机性基础之上的。两个纠缠体系之间的非局域特性就是一种能产生独立于设备的真随机数的理想对象。对于使用最大纠缠的比特对和两个测量装置的标准方案而言,使用投影测量时每轮产生的随机数最多为一个比特。如果允许使用非投影测量,这个限制即可被突破。

最近已有理论证明对称的、信息完备的、正定的算子测量(SIC-POVM)最多可用于两个随机比特的认证。但该理论尚未通过实验验证。

图1 一种基于信息完备正定算子测量的随机性认证实验方案示意图

南京邮电大学量子信息研究团队的刘晨曦,李剑和王琴等在2020年Chinese Optics Letters第18卷第10期(C. Liu, et al., Experimental randomness certification with a symmetric informationally complete positive operator-valued measurement)发表了通过正定算符值测量和最大纠缠态产生多于1 Bit随机数的实验结果。

纠缠态的双光子通过自发参量下的转换过程产生, 单光子偏振态的局域投影测量借助波片、偏振分束器和单光子探测器来实现。而对称的,信息完备的正定算符值的特殊测量,则是通过包含一组波片和光束偏移器的量子行走装置来实现。

为了确认实验中的量子纠缠和相应的各种测定,实验对一个有效Bell不等式进行了测量。该不等式的经典界是4,而最大量子违背值为4\sqrt(3)。实验实测的结果为6.7998,非常接近量子极限,这有效保证了实验中每轮测量可以产生多余1Bit的真随机数。

王琴教授认为,这种使用量子非局域性和非投影测量的量子随机数发生器是一种更为有效的方法,未来有望认证为设备无关随机数发生器(DI-RNG),即最安全的随机数发生器,必将在保密通信等关键领域发挥重要作用。

Experimental randomness certification with a symmetric informationally complete positive operator-valued measurement

Random numbers are important resources in science, engineering and even economics. Methods based on some deterministic algorithm and some randomness seed in most computers, can produce numbers with random statistic distribution, but be possibly predicted in principle, which is called pseudorandom number generator. However, the true random numbers can be generated from unpredictable physical events, guaranteed by the intrinsic randomness of some physical processes.

Quantum random number generator (QRNG) is based on the inherent randomness of quantum mechanics. The nonlocality of two entangled subsystems provides a good candidate to generate true random numbers independent of the devices. For the standard protocol with two measurement devices and a maximally-entangled two-qubit system, the maximal random number generated via local projective measurements is one bit per round. If non-projective measurement is allowed, the bound can be exceeded. Recently, Andersson et al. proved that a symmetric, informationally complete, positive operator-valued measurement (SIC-POVM) can be used for the certification of two random bits at most.

Fig. 1: Schematic of the experimental setup for randomness certification based on SIC-POVM.

The experiment introduced by Mr. Chenxi Liu from a research group led by Prof. Jian Li and Prof. Qin Wang of Nanjing University of Posts and Telecommunications in Chinese Optics Letters, Volume 18, Issue 10, 2020 (C. Liu, et al., Experimental randomness certification with a symmetric informationally complete positive operator-valued measurement) is a demonstration of randomness generation more than one bit via positive operator-valued measurements (POVM) and maximally-entangled state.

The two-photon in entangled state is generated via spontaneous parametric down-conversion process. The local projective measurements on the polarization states of single photon are realized by wave plates, polarization beam splitters and single photon detectors. A quantum walk setup is built with wave plates and beam displacers to perform the symmetric informationally-complete positive operator-valued measurement, a special non-projective measurement. To ensure the entanglement and corresponding measurements, an elegant Bell inequality is measured in the experiment. The classical bound of the inequality is 4, while the maximum quantum violation is 4\sqrt(3). The experimental result is about 6.7998, close to the quantum bound, which guarantees more than one bit randomness can be generated per round in the experiment.

Prof. Qin Wang from Nanjing University of Posts and Telecommunications believes that the QRNG with quantum nonlocality and non-projective measurement is more efficient. And it can be further certified to be device-independent (DI), where device-independent - random number generator (DI-RNG), as the most secure random number generator, would play an important role in some key areas, such as secure communication.