Generation of Fresh and Pure Random Numbers for Loophole-Free Bell Tests

Abstract

We demonstrate extraction of randomness from spontaneous-emission events less than 36 ns in the past, giving output bits with excess predictability below 10 −5 and strong metrological randomness assurances. This randomness generation strategy satisfies the stringent requirements for unpredictable basis choices in current "loophole-free Bell tests" of local realism [Hensen et al., Nature (London) 526, 682 (2015); Giustina et al., Phys. Rev. Lett. 115, 250401 (2015); Shalm et al., Phys. Rev. Lett. 115, 250402 (2015)].PACS numbers: 03.65.Ud, 03.65.Ta, 42.50.Ct, Quantum nonlocality [1] is one of the most striking predictions to emerge from quantum theory. Beyond their fundamental interest, loophole-free Bell tests enable powerful "device independent" information protocols, guaranteed by the impossibility of faster-than-light communication [2]. Bell tests and device-independent protocols employ spacelike separation of measurements to guarantee the nonlocality of correlations [3][4][5][6][7][8] and the monogamy of correlations under the no-signaling principle [9][10][11]. To be secure, they must close two spacetime loopholes: no basis choice may influence a distant particle (locality loophole), and the entanglement generation must not influence the basis choices (freedom-ofchoice loophole). Current efforts [6,7,[12][13][14] to simultaneously close the detection [4,6,7], locality [3], and freedom-of-choice (FoC) [5,8] loopholes require random number generators (RNGs) with an unprecedented combination of speed, unpredictability, and confidence [15][16][17].Here we combine ultrafast RNG by accelerated laser phase diffusion [18][19][20] with real-time randomness extraction and metrological randomness assurances [21] to produce a RNGs suitable for loophole-free Bell tests. Because the laser phase diffusion is driven by effects, including spontaneous emission, that are unpredictable both in quantum theory and in an important class of stochastic hidden variable theories, the source can be used to address the "freedom-of-choice" loophole [22]. Using a detailed and validated model of the signal generation process, we show the effectiveness of parity-bit randomness extraction of this source. Under paranoid assumptions, we infer excess predictability below 10 −5 at 6σ statistical confidence for output based on phase-diffusion events less than 36 ns old. A statistical analysis based on 2.3 Tbits of random data supports the metrological assessment of extreme unpredictability. The results enable definitive nonlocality experiments and secure communications without the need for trusted devices [9,11,23,24].As shown in Fig. 1, the locality and freedom-of-choice loopholes can be closed by spacelike separation of the random events that determine the basis choice from the distant detection and from the production of the pairs of particles, respectively [10]. This requires generation of randomness in a time window shorter than the light time between the detectors. Closing the "detection loophole" requires high efficiency and motivates p...

Requirements for a loophole-free photonic Bell test using imperfect setting generators

“…To preserve the statistical conclusions, the used values of A , B , and p 11 should be conservative overestimates, while p 12 , p 21 , p 22 should be conservative underestimates. Estimates of this kind, including p-values for A , B have recently been reported for phase-diffusion random number generators [52,58]. The p-value for A , B can be taken into account by including the failure probability q f into the process counting procedure, explained in the previous paragraph.…”

“…For random number generators with small bias [52,58], it might be more efficient to quantify with A , B the excess predictability beyond probability 1 2 , despite the presence of the bias. Expression (16) then becomes 1 2 (1 − A ) ≤ p(a|µ) ≤ 1 2 (1 + A ), and similar for Bob.…”

“…Candidate stochastic processes include chaotic dynamics, human decision-making [42], and cosmic light sources [47]. Photonic devices use the reflection/transmission at a beam splitter [48] or the emission/detection time [49], population [50], or phase [51,52] of a coherent light source. It bears repeating that a local realist model must contain some stochastic element if it is to be testable.…”

Random numbers from vacuum fluctuations

“…Such measurements have a very high bandwidth compared to schemes based on photon counting 7,9 , and have a much simpler optical setup compared to phase noise measurements [21][22][23][24][25] . Coupled with an efficient randomness extractor, we obtain an unbiased, uncorrelated stream of random bits at high speed.…”

“…Since the reflection/transmission of the photon is intrinsically random due to the quantum nature of the process, the unpredictability of the generated numbers is ensured 14 . Other implementations of QRNGs measure the amplified spontaneous emission 15 , the vacuum fluctuations of the electromagnetic field [16][17][18] , or the intensity 19,20 and phase noise of different light sources [21][22][23][24][25] .…”