Experimental fast quantum random number generation using high dimensional entanglement with semi self testing
A quantum random number generator (QRNG) generates genuine randomness from the intrinsic probabilistic nature of quantum mechanics. The central problems for most QRNGs are estimating the entropy of the genuine randomness and producing such randomness at high rates. Here we propose and demonstrate a fast semi self testing QRNG at a rate of 24 Mbit/s based on a high dimensional entanglement system, in which the user monitors the entropy in real time via the observation of a nonlocal quantum interference. Our work provides a practical approach to a robust QRNG with trusted but error prone devices. Introduction. Randomness is indispensable for information processing. Quantum random number generators (QRNGs) can generate true randomness by exploiting the fundamental indeterminism of quantum mechanics [1] Most current QRNGs are photonic systems built with trusted and calibrated devices [2] and provide Gbit/s generation speeds at relatively low cost. However, a central issue in these QRNGs is how to certify and quantify the entropy of the genuine randomness, i.e. the randomness that originates from the intrinsic unpredictability of measurements in quantum mechanics. Entropy estimates for specific setups were recently proposed using sophisticated theoretical models [3] Nevertheless, these techniques require parameter characterization which may be difficult to accurately assess in practice. An elegant solution to estimating the entropy is the device independent (DI) or self testing QRNG [1, 4, 5] but its practical implementation is challenging because it requires loophole free violation of Bell's inequality, resulting in low generation rates of ~1 bit/s [1, 5] Recently, Lunghi et al. proposed a more practical solution without the need for Bell violation [6] which can be termed semi self testing, in which the randomness can be guaranteed based on a few general assumptions that do not require detailed device characterization. This scheme is highly desirable as it focuses on real world implementations with trusted but error prone devices, although its implementation to date still suffers from low generation rates of tens of bits/s [6] In this work, based on high dimensional entanglement, we propose and experimentally demonstrate a simple, practical and fast semi self testing QRNG at a rate over 24 Mbits/s. The amount of genuine quantum randomness is quantified directly from observation of a nonlocal interference and a pair of incompatible quantum measurements, and it is separated from other sources of randomness such as technical noise with a randomness extractor. We achieved the high generation rate by virtue of a number of experimental features: a high dimensional time energy entangled photon source capable of producing multiple random bits per photon, a high visibility Franson interferometer for evaluating entanglement, and high efficiency superconducting nanowire single photon detectors (SNSPDs) Protocol. An entanglement source is used to generate high dimensional entangled photon pairs. In the ideal case, the Nd dimensional entangled state can be written as |ps> 1 Nd Nd 1 i=0 |i> A |i> B. (1) This state is observed by two measurement systems A and B. The randomness is generated from A, while B is used to test the states. To model imperfections, we assume that the state rA of system A is not pure and is correlated with environmental noise. Using the same concept as the semi self testing QRNG [6] we assume the devices in the protocol are not deliberately designed to fool the user, but the implementation may be imperfect. The central task is to estimate the amount of genuine randomness based only on measurements. This is a nontrivial task as the observed randomness can have different origins. If the state rA is a superposition of high dimensional states, then the outcome Ri cannot be predicted with certainty, even if the internal state is known, thus resulting in genuine quantum randomness. On the other hand, the randomness may be due to technical imperfections such as detector noise and temperature fluctuations, whose randomness clearly contains no quantum randomness, since the outcome Ri can be perfectly guessed if the imperfections were well quantified. In our approach, the amount of genuine randomness is quantified via the uncertainty relation [7, 8] from a pair of incompatible quantum measurements, namely time measurement T and frequency measurement W. T is realized by directly measuring the photon's arrival time, while W is performed by Franson interferometry [9] In particular, the Franson visibility V is used to bound the randomness. Classical fields result in V that is no greater than 50% For a maximally entangled state, V would be unity in the ideal case [9, 10] Conceptually, V 50% guarantees that the source's output is entangled and thus contains genuine randomness. More rigorously, Ref. [11] has proved that V provides an explicit bound for the correlations in W, under the assumption that the quantum state is Gaussian, which in turns bounds the conditional maximum entropy (given system B) in W via the theory developed in [8] By using the entropic uncertainty relation for smooth entropies [7] we can determine the conditional min entropy given the environmental noise and thus the guessing probability, i.e. the amount of genuine randomness. Our protocol provides self monitoring because measurements of V directly quantify the amount of genuine randomness in the observed data. A threshold value V0 is pre selected and the randomness can be generated only when the observation satisfies V V0. Two particular advantages of this approach are: (i) the observation of V does not rely on detailed models of the devices that are employed; and (ii) no loophole free Bell inequality violation is required. Experiment. Figure 1 shows our experimental setup. It uses a high dimensional time energy entanglement source based on spontaneous parametric down conversion (SPDC) in a PPKTP waveguide [12] which supports multiple spatial modes at telecom wavelengths. The 46.1 mm grating period was designed for type II quasi phase matched wavelength degenerate outputs at 1560 nm in the fundamental modes of the signal C HWP PBS Diode Laser