Strong experimental guarantees in ultrafast quantum random number generation

Abstract

We describe a methodology and standard of proof for experimental claims of quantum random-number generation (QRNG), analogous to well-established methods from precision measurement. For appropriately constructed physical implementations, lower bounds on the quantum contribution to the average min-entropy can be derived from measurements on the QRNG output. Given these bounds, randomness extractors allow generation of nearly perfect " -random" bit streams. An analysis of experimental uncertainties then gives experimentally derived confidence levels on the randomness of these sequences. We demonstrate the methodology by application to phase-diffusion QRNG, driven by spontaneous emission as a trusted randomness source. All other factors, including classical phase noise, amplitude fluctuations, digitization errors, and correlations due to finite detection bandwidth, are treated with paranoid caution, i.e., assuming the worst possible behaviors consistent with observations. A data-constrained numerical optimization of the distribution of untrusted parameters is used to lower bound the average min-entropy. Under this paranoid analysis, the QRNG remains efficient, generating at least 2.3 quantum random bits per symbol with 8-bit digitization and at least 0.83 quantum random bits per symbol with binary digitization at a confidence level of 0.999 93. The result demonstrates ultrafast QRNG with strong experimental guarantees.

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

“…Here we develop statistical metrology for a short-delay RNG, in analogy to earlier work with high-throughput RNGs [19,21,28]. The excess predictability is exponentially reduced by randomness extraction (RE) [29]: in real time, we compute the parity of several raw bits to produce one very unpredictable extracted bit for the setting choice.…”

“…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].…”

“…delayed contributions from earlier pulses [21], and v PD is the detector noise. v φ = 2V √ v S v L cos φ is the trusted signal from interference, where V is the visibility after detection.…”

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.…”