Quantum Information Processing ( IF 2.5 ) Pub Date : 2021-05-03 , DOI: 10.1007/s11128-021-03110-3 Myriam Nonaka , Marcelo Kovalsky , Mónica Agüero , Alejandro Hnilo
The generation of series of random numbers is an important and difficult problem. Appropriate measurements on entangled states have been proposed as the definitive solution. In principle, this solution requires reaching the challenging “loophole-free” condition, which is unattainable in a practical situation nowadays. Yet, it is intuitive that randomness should gradually deteriorate as the setup deviates from that ideal condition. In order to test whether this trend exists or not, we prepare biphotons with three different levels of entanglement: moderately entangled (\(S = 2.67\)), marginally entangled (\(S = 2.06\)), and non-entangled (\(S = 1.42\)) in a setup that mimics a practical situation. The indicators of randomness we use here are: a battery of standard statistical tests, Hurst exponent, an evaluator of Kolmogorov complexity, Takens’ dimension of embedding, and augmented Dickey–Fuller and Kwiatkowski–Phillips–Schmidt–Shin to check stationarity. A nonparametrical statistical ANOVA (Kruskal–Wallis) analysis reveals a strong influence of the level of entanglement with randomness when measured with Kolmogorov complexity in three time series with P-values and strength factor \(\epsilon ^2\): \(P = 0.0015\), \(\epsilon ^2 = 0.28\); \(P = 4.5\times 10^{-4}\), \(\epsilon ^2 = 0.67\) and \(P = 5.6\times 10^{-4}\), \(\epsilon ^2 = 0.16\). The setup is pulsed with time stamping, what allows generate different series applying different methods with the same data, even after the experimental run has ended, and to compare their raw randomness. It also allows the stroboscopic reconstruction of time variation of entanglement.
中文翻译:
在实际设置中测试不同程度的纠缠如何影响可预测性
随机数序列的产生是一个重要而困难的问题。已经提出了对纠缠态的适当测量作为确定的解决方案。原则上,此解决方案需要达到具有挑战性的“无漏洞”条件,这在当今的实际情况下是无法实现的。然而,很直观的是,随着设置偏离理想条件,随机性应逐渐恶化。为了测试这种趋势是否存在,我们准备了具有三种不同纠缠度的双光子:中等纠缠度(\(S = 2.67 \)),轻微纠缠度(\(S = 2.06 \))和非纠缠度(\(S = 2.06 \))。\(S = 1.42 \)),以模仿实际情况。我们在这里使用的随机性指标是:一组标准统计检验,赫斯特指数,一个Kolmogorov复杂度评估器,Takens的嵌入维数以及增强的Dickey-Fuller和Kwiatkowski-Phillips-Schmidt-Shin来检查平稳性。当与Kolmogorov复杂在具有三个时间序列测量的nonparametrical统计ANOVA(秩和检验)分析揭示了与随机性缠结的水平的强烈影响P -值和强度因子\(\小量^ 2 \) :\(P = 0.0015 \),\(\ε^ 2 = 0.28 \) ; \(P = 4.5 \乘以10 ^ {-4} \),\(\ epsilon ^ 2 = 0.67 \)和\(P = 5.6乘以10 ^ {-4} \),\(\ epsilon ^ 2 = 0.16 \)。该设置带有时间戳记,可以在实验运行结束后使用具有相同数据的不同方法生成不同的序列,并比较它们的原始随机性。还可以通过频闪仪重建纠缠的时间变化。