Random-bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require ``strong'' RBGs that produce high-entropy bit sequences, but traditional software pseudo-RBGs have very low entropy content and therefore are relatively weak for cryptography. Hardware RBGs yield entropy from chaotic or quantum physical systems and therefore are expected to exhibit high entropy, but in current implementations their exact entropy content is unknown. Here we report a quantum random-bit generator (QRBG) that harvests entropy by measuring single-photon and entangled two-photon polarization states. We introduce and implement a quantum tomographic method to measure a lower bound on the ``min-entropy'' of the system, and we employ this value to distill a truly random-bit sequence. This approach is secure: even if an attacker takes control of the source of optical states, a secure random sequence can be distilled.
Random-bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require strong'' RBGs that produce high-entropy bit sequences, but traditional software pseudo-RBGs have very low entropy content and therefore are relatively weak for cryptography. Hardware RBGs yield entropy from chaotic or quantum physical systems and therefore are expected to exhibit high entropy, but in current implementations their exact entropy content is unknown. Here we report a quantum random-bit generator (QRBG) that harvests entropy by measuring single-photon and entangled two-photon polarization states. We introduce and implement a quantum tomographic method to measure a lower bound on the min-entropy'' of the system, and we employ this value to distill a truly random-bit sequence. This approach is secure: even if an attacker takes control of the source of optical states, a secure random sequence can be distilled.
Randomness is a valuable resource in science, cryptography, engineering, and information technology. Quantum-mechanical sources of randomness are attractive because of the indeterminism of individual quantum processes. Here, we consider the production of random bits from polarization measurements on photons. We first present a pedagogical discussion of how the quantum randomness inherent in such measurements is connected to quantum coherence, and how it can be quantified in terms of the quantum state and an associated entropy value known as min-entropy. We then explore these concepts by performing a series of single-photon experiments that are suitable for the undergraduate laboratory. We prepare photons in different nonentangled and entangled states, and measure these states tomographically. We use the information about the quantum state to determine, in terms of the min-entropy, the minimum amount of randomness produced from a given photon state by different bit-generating measurements. This is helpful in assessing the presence of quantum randomness and in ensuring the quality and security of the random-bit source.
This paper presents the design and theoretical framework for a quantum random number generator (QRNG) rooted in the principles of quantum mechanics. The core innovation lies in leveraging the inherent randomness associated with quantum measurement, specifically the uncertainty principle, to generate truly random numbers, a significant departure from the limitations of classical random number generators. The proposed system utilizes a measurement process involving a quantum system, such as a photon polarization or a quantum bit, to produce a sequence of random bits. The generated bits are then processed to eliminate bias and ensure high uniformity. The theoretical analysis focuses on quantifying the randomness inherent in the measurement process and demonstrating the potential for generating high-quality random numbers. This work addresses the growing demand for secure communication, cryptography, and simulation applications that require truly random numbers, offering a fundamentally different approach compared to traditional methods.
Generation of random numbers is a central problem for many applications in the field of information processing, including, e.g., cryptography, in classical and quantum regime, but also mathematical modeling, Monte Carlo methods, gambling and many others. Both, the quality of the randomness and efficiency of the random numbers generation process are crucial for the most of these applications. Software produced pseudorandom bit sequences, though sufficiently quick, do not fulfill required randomness quality demands. Hence, the physical hardware methods are intensively developed to generate truly random number sequences for information processing and electronic security application. In the present paper we discuss the idea of the quantum random number generators. We also present a variety of tests utilized to assess the quality of randomness of generated bit sequences. In the experimental part we apply such tests to assess and compare two quantum random number generators, PQ4000KSI (of company ComScire US) and JUR01 (constructed in Wroclaw University of Science and Technology upon the project of The National Center for Research and Development) as well as a pseudorandom generator from the Mathematica Wolfram package. Finally, we present our new prototype of fully operative miniaturized quantum random generator JUR02 producing a random bit sequence with velocity of 1 Mb/s, which successfully passed standard tests of randomness quality (like NIST and Dieharder tests). We also shortly discuss our former concept of an entanglement-based quantum random number generator protocol with unconditionally secure public randomness verification.
Random numbers are one of the key foundations of cryptography. This work implements a discrete quantum random number generator (QRNG) based on the tunneling effect of electrons in an avalanche photo diode. Without any post-processing and conditioning, this QRNG can output raw sequences at a rate of 100 Mbps. Remarkably, the statistical min-entropy of the 8,000,000 bits sequence reaches 0.9944 bits/bit, and the min-entropy validated by NIST SP 800-90B reaches 0.9872 bits/bit. This metric is currently the highest value we have investigated for QRNG raw sequences. Moreover, this QRNG can continuously and stably output raw sequences with high randomness over extended periods. The system produced a continuous output of 1,174 Gbits raw sequence for a duration of 11,744 s, with every 8 Mbits forming a unit to obtain a statistical min-entropy distribution with an average value of 0.9892 bits/bit. The statistical min-entropy of all data (1,174 Gbits) achieves the value of 0.9951 bits/bit. This QRNG can produce high-quality raw sequences with good randomness and stability. It has the potential to meet the high demand in cryptography for random numbers with high quality.
Random number generators are employed for stochastic simulations and
cryptography. Besides the quality of randomness, a crucial aspect for
applications is security, namely the monitoring of the lower bound on the
entropy produced by the generator in any context, even fraudulent ones. In this
regard, quantum entanglement represents an ideal resource, because it provides
non-classical correlations between intrinsically random outcomes. However,
entanglement-based certified random numbers generators are particularly
challenging from a practical point of view. Here, we demonstrate a new
certified quantum random number generator based on momentum-polarization
entangled single photon states. The use of single particle entanglement allows
employing an attenuated laser source and a simple setup where only linear
optical components are utilized. A semi-device independent modeling of the
photonic quantum random number generator certifies a minimum entropy of (2.5±0.5)%, corresponding to a generation rate of 4.4 kHz. Modeling the
generation stage of the setup permits to increase the certified minimum entropy
to (30.1±0.5)%, implying a generation rate of 52.7 kHz, at the expenses
of an increased level of trust on the system.
Quantum entanglement represents an ideal resource to guarantee the security of random numbers employed in many scientific and cryptographic applications. However, entanglement-based certified random number generators are particularly challenging to implement. Here, we demonstrate a certified quantum random number generator based on momentum-polarization entangled single-photon states. The use of single-photon entanglement allows an attenuated laser source to be employed and a simple setup where only linear optical components are utilized. For the latter, a semi-device-independent modeling of the photonic quantum random number generator is developed, which certifies a minimum entropy of $(2.5\ifmmode\pm\else\textpm\fi{}0.5)\mathrm{%}$, corresponding to a generation rate of 4.4 kHz. At the expenses of a higher level of trust in the system, the certified minimum entropy can be increased to $(30.1\ifmmode\pm\else\textpm\fi{}0.5)\mathrm{%}$, implying a generation rate of 52.7 kHz. Our results show that a simple optical implementation combined with an accurate modeling provide an entanglement-based high-security quantum random number generator using imperfect devices.