Certified private randomness can be extracted by a system that show a violation of a Bell inequality. The randomness extraction rate depends on the observed violation and on the repetition rate of the Bell test. Photonic systems generally show a smaller violation, but thanks to their higher repetition it is possible to obtain higher randomness generation rate. We demonstrate a detection loophole-free Bell violation using a photonic system based on a continuous wave source, and show that it allows to increase the randomness generation rate compared to pulsed systems.
Certified private randomness can be extracted by a system that show a violation of a Bell inequality. The randomness extraction rate depends on the observed violation and on the repetition rate of the Bell test. Photonic systems generally show a smaller violation, but thanks to their higher repetition it is possible to obtain higher randomness generation rate. We demonstrate a detection loophole-free Bell violation using a photonic system based on a continuous wave source, and show that it allows to increase the randomness generation rate compared to pulsed systems.
Quantum physics can provide sources of randomness that can be certified as being uncorrelated to any outside process or variable, i.e. sources of private randomness, based on a violation of a Bell inequality. Initial experimental realizations of such sources of certified randomness are based on atomic or atomic-like systems, but suffer from impractically low generation rates for most applications. High efficiency infrared photodetectors and photon pair sources permitted experimental demonstrations of loophole free violation of the Bell inequality using photons. The random bit generation rate for these setups was on the order of tens per second, where the main limitation is the fixed repetition rate of the photon pair source combined with the small violation observed. In our experiment, we close the detection loophole with a system efficiency over 82%. The source of entangled photon pairs is based on continuously pumped spontaneous parametric down conversion. We estimate a collection efficiency of ≈90% into single mode fibers and detect photons with a transition edge sensors. Detection events are time-tagged and organized into time bins, for which we consider four possible outcomes: one or more detections at Alice’s side, one or more detections at Bob’s side, one or more detections at both Alice’s and Bob’s, and no detection in either channel. These events eventually lead to a CHSH-type Bell inequality that is violated for a range of time bin widths. With such an arrangement, we reach asymptotic device-indepentnet random bit generation rates on the order of 1000 bits per second.
We present a violation of the Clauser-Horne-Shimony-Holt inequality without the fair sampling assumption with a continuously pumped photon pair source combined with two high efficiency superconducting detectors. Because of the continuous nature of the source, the choice of the duration of each measurement round effectively controls the average number of photon pairs participating in the Bell test. We observe a maximum violation of S=2.016 02(32) with an average number of pairs per round of ≈0.32, compatible with our system overall detection efficiencies. Systems that violate a Bell inequality are guaranteed to generate private randomness, with the randomness extraction rate depending on the observed violation and on the repetition rate of the Bell test. For our realization, the optimal rate of randomness generation is a compromise between the observed violation and the duration of each measurement round, with the latter realistically limited by the detection time jitter. Using an extractor composably secure against quantum adversary with quantum side information, we calculate an asymptotic rate of ≈1300 random bits/s. With an experimental run of 43 min, we generated 617 920 random bits, corresponding to ≈240 random bits/s.
Abstract From dice to modern electronic circuits, there have been many attempts to build better devices to generate random numbers. Randomness is fundamental to security and cryptographic systems and to safeguarding privacy. A key challenge with random-number generators is that it is hard to ensure that their outputs are unpredictable1–3. For a random-number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model that describes the underlying physics is necessary to assert unpredictability. Imperfections in the model compromise the integrity of the device. However, it is possible to exploit the phenomenon of quantum non-locality with a loophole-free Bell test to build a random-number generator that can produce output that is unpredictable to any adversary that is limited only by general physical principles, such as special relativity1–11. With recent technological developments, it is now possible to carry out such a loophole-free Bell test12–14, 22. Here we present certified randomness obtained from a photonic Bell experiment and extract 1, 024 random bits that are uniformly distributed to within 10−12. These random bits could not have been predicted according to any physical theory that prohibits faster-than-light (superluminal) signalling and that allows independent measurement choices. To certify and quantify the randomness, we describe a protocol that is optimized for devices that are characterized by a low per-trial violation of Bell inequalities. Future random-number generators based on loophole-free Bell tests may have a role in increasing the security and trust of our cryptographic systems and infrastructure.
Bell inequality violations can be used to certify private randomness for use in cryptographic applications. In photonic Bell experiments, a large amount of the data that is generated comes from no-detection events and presumably contains little randomness. This raises the question as to whether randomness can be extracted only from the smaller post-selected subset corresponding to proper detection events, instead of from the entire set of data. This could in principle be feasible without opening an analogue of the detection loophole as long as the min-entropy of the post-selected data is evaluated by taking all the information into account, including no-detection events. The possibility of extracting randomness from a short string has a practical advantage, because it reduces the computational time of the extraction. Here, we investigate the above idea in a simple scenario, where the devices and the adversary behave according to i.i.d. strategies. We show that indeed almost all the randomness is present in the pair of outcomes for which at least one detection happened. We further show that in some cases applying a pre-processing on the data can capture features that an analysis based on global frequencies only misses, thus resulting in the certification of more randomness. We then briefly consider non-i.i.d strategies and provide an explicit example of such a strategy that is more powerful than any i.i.d. one even in the asymptotic limit of infinitely many measurement rounds, something that was not reported before in the context of Bell inequalities.
What is the most efficient way to generate random numbers device-independently using a photon pair source based on spontaneous parametric down conversion? We consider this question by comparing two implementations of a detection-loophole-free Bell test. In particular, we study in detail a scenario where a source is used to herald path-entangled states, i.e. entanglement between two spatial modes sharing a single photon and where non-locality is revealed using photon counting preceded by small displacement operations. We start by giving a theoretical description of such a measurement. We then show how to optimize the Bell–CHSH violation through a non-perturbative calculation, taking the main experimental imperfections into account. We finally bound the amount of randomness that can be extracted and compare it to the one obtained with the conventional scenario using photon pairs entangled e.g. in polarization and analyzed through photon counting. While the former requires higher overall detection efficiencies, it is far more efficient in terms of the entropy per experimental run and under reasonable assumptions, it provides higher random bit rates.
We present a source of entangled photons that violates a Bell inequality free of the "fair-sampling" assumption, by over 7 standard deviations. This violation is the first reported experiment with photons to close the detection loophole, and we demonstrate enough "efficiency" overhead to eventually perform a fully loophole-free test of local realism. The entanglement quality is verified by maximally violating additional Bell tests, testing the upper limit of quantum correlations. Finally, we use the source to generate "device-independent" private quantum random numbers at rates over 4 orders of magnitude beyond previous experiments.