Piotr Jóźwiak

Recent experimental implementations of publicly verifiable quantum random number generators (PV-QRNGs) based on quantum entanglement reflect growing interest in this emerging paradigm of QRNG technology, originally proposed in our earlier work. These implementations employ specific representatives of entangled multi-qubit state families defined by us, which enable public verification of randomness without revealing the generated strings. PV-QRNGs address the limitations of local computational testing and offer enhanced scalability and reliability. This approach is especially relevant in the context of quantum and post-quantum cryptography, where the certification of high-quality randomness is essential. We present the theoretical foundations of PV-QRNGs and explore their potential to advance secure, scalable, and transparently verifiable quantum randomness generation.

Two new concepts of quantum random number generators (QRNG) are presented. The first one is related with the application of quantum entanglement to producing several mutually coupled in a random manner bit sequences, which can be used in cryptographic applications and verified in a parallel manner allowing for entropy measurement in real time in public domain using arbitrary large resources for patterns detection, but without compromising the secrecy of coupled by quantum entanglement dual random binary sequences. This is a new concept for verification of fidelity of random bit sequences in a fully non-destructive way, allowing for various applications of generated random bits for which secrecy is important (e.g. in cryptograhic applications). The idea is the development of former our proposal [1]. The second concept is reletad to our progress in prototyping of miniaturized QRNG utilizing the quantum transitions allong the Fermi golden rule as the entropy source, developed for application to quantum cryptography (QKD) systems based on continuous variables. The prototype exploiting, as the source of the entropy, the photoelectric process in a photodiode coupled to a small LED is miniaturized to size of 2 cm [2] and produces the random sequence with a rate of 1 Mb/s. We present current developments of the concept towards its further miniaturization to sizes suitable for using this QRNG device in portable computers, mobile phones and miniaturized terminals for QKD using non-entangled photons. 1. Janusz E. Jacak, Witold A. Jacak, Wojciech A. Donderowicz, Lucjan Jacak, Quantum random number generators with entanglement for public randomness testing, Scientific Reports, (2020) 10:164, https://doi.org/10.1038/s41598-019-56706-2 2. Marcin M. Jacak, Piotr Jóźwiak, Jakub Niemczuk, Janusz E. Jacak, Quantum generators of random numbers, Scientific Reports, (2021) 11:16108, https://doi.org/10.1038/s41598-021-95388-7

Validation of the randomness of a quantum random number generator (QRNG) can be performed via robust statistical testing, which generally reduces to the problem of finding long range patterns in the generated random bit sequence. This problem is computationally exhaustive and poses one of important challenges for industrial implementation of self-testing integrated QRNG devices. Furthermore, classical statistical testing cannot in principle confirm the quantum non-determinism (from which the QRNG device can deviate due to its implementation imperfections). Instead, classical testing can confirm that up to certain parameters threshold, deterministic patterns were not detected. The device independent QRNG schemes are based on quantum entanglement, which is a non-classical resource that can be verified in terms of quantum measurements non-classical correlations statistically violating Bell type (e.g. CHSH) inequalities for classical limits on such correlations. This reults in a fundamental (independent from a technical implementation) confirmation that the process used to generate randomness based on entangled quantum states is indeed non-deterministic. In this paper we describe a series of recent experimental developments focused on generating quantum entanglement based randomness in a quntum optics device-independent approach, with validation of the randomness through experimentally verified violation of the CHSH inequality [1]. The experimental setup for entanglement based QRNG involves generation of entanglement in photon polarizations in the SPDC type II process with a single-photon detectors (SPAD) for quantum measurements of entangled photons. Statistical processing of the measurements outcomes shows violation of the classical limits on the correlations, violating the CHSH inequality and hence proving that the QRNG generated randomness is based on a quantum, non-deterministic process. The further direction for this research is towards miniaturization of the robust quantum optics setups to be more adequate for integrated entanglement QRNG devices. This work is part of the NCBR research and development project (contract no. POIR.01.01.01-00-0173/15) aimed at advancing QRNG setups with technical achievements reported in the SeQre.net platform [2]. 1. J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett., 23 (15): 880–4, doi: https://doi.org/10.1103%2FPhysRevLett.23.880, (1969) 2. SeQre.net, Quantum Cryptography R&D Platform managed by the Department of Quantum Technology at WUST and CompSecur / SeQre, https://seqre.net/qrng

We present a simple idealistic quantum entanglement based protocol for quantum random number generation allowing a trusted third party to publicly perform arbitrarily complex tests of randomness without any violation of the secrecy of the generated bit sequences. The protocol diminishes also an average time of the randomness testing (thus enabling arbitrary shortening of this time with increasing number of entangled qubits).