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Quantum Photonic Devices

Randomness generation from a CHSH violation on entangled photon pairs from a continuous source without fair sampling assumptions (Conference Presentation)

Christian Kurtsiefer

Published Sep 18, 2018• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2325104

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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.
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.
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.
Summary form only given. In a Bell experiment, one prepares pairs of entangled particles and sends them to two observers, Alice and Bob, for measurement and detection [1]. For some choices of their measurement settings, Alice and Bob may observe strong correlations between their results in accordance with the predictions of quantum mechanical theory. Conversely, any physical theory that assumes no physical influence can be faster than the speed of light and that properties of physical systems are elements of reality [2] - a local realistic theory - can predict only a limited amount of correlation between Alice's and Bob's measurement outcomes. Upon observing correlations sufficient to violate Bell's inequality, Alice and Bob must abandon local realism.It is common that in an experiment, some particles emitted by the source will not be detected. Then the subset of detected particles might display correlations that violate the Bell inequality although the entire ensemble can be described by a local realistic theory [3]. To achieve a conclusive Bell violation without assuming that the detected particles are a “fair” sample, a highly efficient setup is necessary. Due to experimental limitations, fair sampling has been assumed in most Bell experiments performed to date, and it has never been possible to avoid this assumption with photons due to the absence of efficient sources and detectors. Here we report the first Bell experiment with photons that does not rely on any fair-sampling assumption. In our experiment we employ the Eberhard inequality, a Bell inequality that by construction does not rely on the fair-sampling assumption [4]. Our source of entangled photon pairs utilizes bulk-crystal spontaneous parametric downconversion in a Sagnac configuration, which has shown to be very efficient [5, 6]. For photon detection, we employ superconducting transition-edge sensors, which not only offer high efficiency but also are intrinsically free of dark counts [7]. This combination of features is imperative for an experiment in which no correction of count rates can be tolerated. We achieve uncorrected coupling efficiencies over 73% in each arm of our source, facilitating a violation of the inequality by nearly 70 standard deviations after five minutes of measurement. Since the first experimental Bell test, a satisfactory laboratory realization of the motivating gedankenexperiment has remained an outstanding challenge. The two other main assumptions include “locality” [8, 9] and “freedom of choice” [10]. Invoking any of these renders an experiment vulnerable to explanation by a local realistic theory. The realization of an experiment that is free of all three assumptions-a so-called loopholefree Bell test-remains an important outstanding goal for the physics community with strong implications for quantum technologies. We note that with our experiment, photons are the first physical system for which each of these three assumptions has been successfully addressed, albeit in different experiments. This represents promise for practical applications like one-sided device-independent quantum key distribution [11], and in an additional test, we also demonstrate that our experimental apparatus is capable of implementing this protocol on both sides.
What is the most efficient way to generate random numbers deviceindependently using a photon pair source based on spontaneous parametric down conversion (SPDC)? 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 heralded single photon source (HSPS) is used to herald path-entangled states, i.e. entanglement between two spatial modes sharing a single photon and where nonlocality is revealed using photon counting preceded by small displacement operations. ar X iv :1 40 9. 80 51 v1 [ qu an tph ] 2 9 Se p 20 14 Device-independent quantum random number generator with a photon pair source 2 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 both the entropy per experimental run and the rate of random bit generation. PACS numbers: 03.65.Ud Device-independent quantum random number generator with a photon pair source 3
Abstract Measurement outcomes on quantum systems exhibit inherent randomness and are fundamentally nondeterministic. This has enabled quantum physics to set new standards for the generation of true randomness with significant applications in the fields of cryptography, statistical simulations, and modeling of the nondeterministic behavior in various other fields. In this work, we present a scheme for the generation of multi-bit random numbers using path-entangled single photons. For the experimental demonstration, we generate a path-entangled state using single photons from spontaneous parametric down-conversion (SPDC) and assign a multi-qubit state for them in path basis. One-bit and two-bit random numbers are then generated by measuring entangled states in the path basis. In addition to passing the NIST tests for randomness, we also demonstrate the certification of quantumness and self-certification of quantum random number generator (QRNG) using Clauser, Horne, Shimony and Holt (CHSH) inequality violation. We also record the significantly low autocorrelation coefficient from the raw bits generated and this along with CHSH violation rules out multi-photon events and ensure the protection from photon splitting attack. Distribution of photons along multiple paths resulting in multiple bits from one photon extends the limit on bit generation rate imposed by the detection dead time of the individual detector. Thus, the path-entangled states can generate higher bitrates compared to scheme using entangled photon pair which are limited by the coincidence counts. We demonstrate this by generating a high rate of about 80 Mbps when the single photon detector saturates at around 28 Mcps and still show violation of CHSH inequality.