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 sat
isfies 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)].
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 {epsilon}-random bit streams. An analysis of experimental uncertainties then gives experimentally derived confidence levels on the {epsilon} 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 0.99993. The result demonstrates ultrafast QRNG with strong experimental guarantees.
We apply spin-squeezing techniques to identify and quantify highly multi-partite photonic entanglement in polarization-squeezed light. We consider a practical single-mode scenario, and find that Wineland-criterion polarization squeezing implies entan
glement of a macroscopic fraction of the total photons. A Glauber-theory computation of the observable N-photon density matrix, with N up to 100, finds that N-partite entanglement is observable despite losses and without post-selection. We estimate that existing detectors could observe $sim1000$-partite entanglement from a few dB of polarization squeezing.
An extensive debate on quantum non-demolition (QND) measurement, reviewed in Grangier et al. [Nature, {bf 396}, 537 (1998)], finds that true QND measurements must have both non-classical state-preparation capability and non-classical information-dama
ge tradeoff. Existing figures of merit for these non-classicality criteria require direct measurement of the signal variable and are thus difficult to apply to optically-probed material systems. Here we describe a method to demonstrate both criteria without need for to direct signal measurements. Using a covariance matrix formalism and a general noise model, we compute meter observables for QND measurement triples, which suffice to compute all QND figures of merit. The result will allow certified QND measurement of atomic spin ensembles using existing techniques.
