Quantum randomness certified by different quantum phenomena

Abstract

Quantum random number generation utilizes quantum processes, which involve the collapse of a superposition state upon performing a measurement. In a quantum process, the measurement outcome is fundamentally unpredictable, resulting in true randomness in the generated numbers. We refer to this type of random number generator as a quantum random number generator (QRNG) since quantum processes are involved in generating random numbers. The most common QRNG is the photonic QRNG. In this kind of QRNG, photons from a laser source go into a beamsplitter. After the beamsplitter, the photons are in a superposition state of reflected path and transmitted path. In each path, there is a detector acting as a measurement device. When a measurement is performed, one photon collapses into one detector randomly, resulting in a click in the detector. The click in the transmitted detector is assigned as raw bit 0, and then the click in the reflected detector is assigned as raw bit 1. Ideally, from this QRNG, each random number generated is a quantum random number. Still, in the real world, the randomness in the generated random numbers is not pure quantum randomness since it can have other technical causes other than quantum mechanics. For example, the click events on the two detectors can come from the dark counts, which are considered to be classical noise. We need to utilize some quantum phenomena, which cannot be explained classically, to prove quantumness in the raw bits to guarantee that the random numbers from the QRNG are all generated by quantum processes instead of some unexpected classical noises. After the quantumness is proved, randomness certification protocols based on this quantumness can be formulated to quantify the entropy of the randomness. This thesis aims to present our progress in constructing randomness certification protocols for QRNGs by leveraging different quantum phenomena to ensure the quantumness of generated random numbers. These quantum phenomena include the single-photon antibunching effect, the wave-particle duality of a delayed-choice experiment, non-locality in a Bell test, and nonzero dimension witness of quantum measurements. In the first approach, a single-photon QRNG based on an nitrogen-vacancy (NV) center is implemented, and three different randomness certification protocols are built to certify quantum randomness in the raw data. In the first model, all the experimental events are used as raw bits to extract randomness, and the randomness output speed is 5.10×10^4 bits per second. In the second model, only single photon events are considered as raw bits, the randomness output speed is 4.74×10^4 bits per second. In the third model only tuple detection events below the unity line are considered raw bits, and the randomness generation speed is 34.37 bits per second. Among them, the second protocol, utilizing the single-photon antibunching effect, achieves a source-independent random number generator without compromising the randomness output speed, making it an ideal protocol for a single-photon QRNG. The second method constructs a QRNG based on a delayed-choice experiment without the fair sampling assumption. Using wave-particle duality, the model ensures photons arrive at detectors in superposition states, eliminating the need for fair sampling. By applying this model to a delayed-choice experiment, we can obtain 1,124 uniformly distributed random bits per second. The third approach certifies quantum randomness from loophole-free Bell test data using Bell's theorem and remote state preparation (RSP)-dimension witness. The RSP-dimension witness model significantly increases the randomness output speed from 2.54 bits per day to 40.63 bits per day, marking an important step towards the practical use of Bell tests in randomness generation. Lastly, a QRNG based on a nuclear spin system inside an NV center is studied, including two randomness certification protocols. The first protocol is a direct application of the W2 model from Lunghi2015, and randomness can be generated with a speed 0.87 bits per second. In the second dimension witness model, we develop a randomness certification protocol based on a three-dimensional dimension witness W3 and its randomness output speed is 1.33 bits per second, which is 53% higher than 0.87 bits per second. By harnessing these four different quantum phenomena, we contribute to the growing need for secure, high-quality random numbers in different fields including cryptography, scientific simulations, and algorithm development.