In role-playing games (RPGs), players are called upon to assume the role of a character moving in an imaginary environment and facing several challenges. Their success or failure often depends on randomizers like cards or dice. Regarding the latter, the most commonly used in RPGs are the Platonic solids with the addition of the ten-sided die. They are commonly simulated through classical computers, however, since true randomness is not in their nature, they can only generate pseudorandom numbers. On the contrary, quantum computers exploit the nondeterministic nature of quantum mechanics, so they are perfect candidates for truly random simulations in games of chance. For this reason, this paper proposes and tests various quantum circuits for sampling uniformly distributed discrete values within a fixed range, corresponding to the number of faces of the dice. The simulations reveal the pure randomness of the output of the implemented circuits. They were then used to generate random numbers within a three-dimensional dice-rolling game.
In role-playing games (RPGs), players are called upon to assume the role of a character moving in an imaginary environment and facing several challenges. Their success or failure often depends on randomizers like cards or dice. Regarding the latter, the most commonly used in RPGs are the Platonic solids with the addition of the ten-sided die. They are commonly simulated through classical computers, however, since true randomness is not in their nature, they can only generate pseudorandom numbers. On the contrary, quantum computers exploit the nondeterministic nature of quantum mechanics, so they are perfect candidates for truly random simulations in games of chance. For this reason, this paper proposes and tests various quantum circuits for sampling uniformly distributed discrete values within a fixed range, corresponding to the number of faces of the dice. The simulations reveal the pure randomness of the output of the implemented circuits. They were then used to generate random numbers within a three-dimensional dice-rolling game.
A coin is just a two sided dice. Recently, Mochon proved that quantum weak coin flipping with an arbitrarily small bias is possible. However, the use of quantum resources to allow N remote distrustful parties to roll an N-sided dice has yet to be addressed. In this paper we show that contrary to the classical case, N-sided dice rolling with arbitrarily small bias is possible for any N. In addition, we present a six-round three-sided dice rolling protocol, achieving a bias of 0.181, which incorporates weak imbalanced coin flipping.
Abstract Quantum mechanics, like other enormously successful physical theories, accurately describes how the natural world behaves. Its explanatory powers regarding the indeterminate behavior of the smallest constituents of nature have proven to be both profound and practical. Many technological devices from lasers to computer chips are based on quantum mechanics. Not surprisingly, the universe filled with microscopic random events revealed by quantum mechanics has generated wonder and interpretive bewilderment. Reactions to the unsettling revelations of quantum unpredictability have included appeals to unknown variables to preserve classical physics, and even wholesale theoretical dismissals. Far from proof of mathematical trickery or theoretical incompletion however, the now well-established and irreducible quantum randomness suggests a physical universe that is open to a future not determined by the past, and perhaps to a God that really does play dice.
The generation of true randomness remains a significant challenge in computer science, particularly when relying solely on classical algorithms. Many current approaches employ pseudo-random number generators (PRNGs), which, despite their computational efficiency, are inherently predictable and lack genuine randomness. This paper proposes a novel method for algorithmic randomness generation leveraging the principles of quantum walks. We demonstrate that the inherent uncertainty and superposition properties of quantum systems provide a robust mechanism for generating truly random numbers. Specifically, we outline a framework for designing quantum walks on graphs, where the evolution of the walker's state is fundamentally probabilistic and unpredictable. The core of our approach resides in exploiting the quantum walk's non-deterministic nature to produce sequences of numbers that exhibit statistical properties consistent with true randomness. The theoretical framework is presented, including a detailed description of the mathematical formalism underlying the quantum walk and the probability distribution of the walker's positions. We highlight the potential advantages of this approach, particularly in scenarios demanding high-quality randomness for cryptographic applications or simulations. The key concept is to translate a classical problem into a quantum one, where the inherent probabilistic nature of quantum mechanics offers a superior solution to the problem of generating genuine randomness.
Random numbers are fundamental elements in different fields of science and technology such as computer simulation like Monte Carlo-method simulation, statistical sampling, cryptography, games and gambling, and other areas where unpredictable results are necessary. Random number generators (RNG) are generally classified as “pseudo”-random number generators (PRNG) and "truly" random number generators (TRNG). Pseudo random numbers are generated by computer algorithms with a (random) seed and a specific formula. The random numbers produced in this way (with a small degree of unpredictability) are good enough for some applications such as computer simulation. However, for some other applications like cryptography they are not completely reliable. When the seed is revealed, the entire sequence of numbers can be produced. The periodicity is also an undesirable property of PRNGs that can be disregarded for most practical purposes if the sequence recurs after a very long period. However, the predictability still remains a tremendous disadvantage of this type of generators. Truly random numbers, on the other hand, can be generated through physical sources of randomness like flipping a coin. However, the approaches exploiting classical motion and classical physics to generate random numbers possess a deterministic nature that is transferred to the generated random numbers. The best solution is to benefit from the assets of indeterminacy and randomness in quantum physics. Based on the quantum theory, the properties of a particle cannot be determined with arbitrary precision until a measurement is carried out. The result of a measurement, therefore, remains unpredictable and random. Optical phenomena including photons as the quanta of light have various random, non-deterministic properties. These properties include the polarization of the photons, the exact number of photons impinging a detector and the photon arrival times. Such intrinsically random properties can be exploited to generate truly random numbers. Silicon (Si) is considered as an interesting material in integrated optics. Microelectronic chips made from Si are cheap and easy to mass-fabricate, and can be densely integrated. Si integrated optical chips, that can generate, modulate, process and detect light signals, exploit the benefits of Si while also being fully compatible with electronic. Since many electronic components can be integrated into a single chip, Si is an ideal candidate for the production of small, powerful devices. By complementary metal-oxide-semiconductor (CMOS) technology, the fabrication of compact and mass manufacturable devices with integrated components on the Si platform is achievable. In this thesis we aim to model, study and fabricate a compact photonic quantum random number generator (QRNG) on the Si platform that is able to generate high quality, "truly" random numbers. The proposed QRNG is based on a Si light source (LED) coupled with a Si single photon avalanche diode (SPAD) or an array of SPADs which is called Si photomultiplier (SiPM). Various implementations of QRNG have been developed reaching an ultimate geometry where both the source and the SPAD are integrated on the same chip and fabricated by the same process. This activity was performed within the project SiQuro—on Si chip quantum optics for quantum computing and secure communications—which aims to bring the quantum world into integrated photonics. By using the same successful paradigm of microelectronics—the study and design of very small electronic devices typically made from semiconductor materials—, the vision is to have low cost and mass manufacturable integrated quantum photonic circuits for a variety of different applications in quantum computing, measure, sensing, secure communications and services. The Si platform permits, in a natural way, the integration of quantum photonics with electronics. Two methodologies are presented to generate random numbers: one is based on photon counting measurements and another one is based on photon arrival time measurements. The latter is robust, masks all the drawbacks of afterpulsing, dead time and jitter of the Si SPAD and is effectively insensitive to ageing of the LED and to its emission drifts related to temperature variations. The raw data pass all the statistical tests in national institute of standards and technology (NIST) tests suite and TestU01 Alphabit battery without a post processing algorithm. The maximum demonstrated bit rate is 1.68 Mbps with the efficiency of 4-bits per detected photon. In order to realize a small, portable QRNG, we have produced a compact configuration consisting of a Si nanocrystals (Si-NCs) LED and a SiPM. All the statistical test in the NIST tests suite pass for the raw data with the maximum bit rate of 0.5 Mbps. We also prepared and studied a compact chip consisting of a Si-NCs LED and an array of detectors. An integrated chip, composed of Si p+/n junction working in avalanche region and a Si SPAD, was produced as well. High quality random numbers are produced through our robust methodology at the highest speed of 100 kcps. Integration of the source of entropy and the detector on a single chip is an efficient way to produce a compact RNG. A small RNG is an essential element to guarantee the security of our everyday life. It can be readily implemented into electronic devices for data encryption. The idea of "utmost security" would no longer be limited to particular organs owning sensitive information. It would be accessible to every one in everyday life.
Generating random numbers plays an important role in many scientific applications. Compared to pseudorandom number generators, a quantum device is capable of generating true random numbers by the laws of quantum mechanics. However, information-theoretical secure random numbers are regularly based on a perfect device model, which may deviate from a real-world device. To close this gap, we propose a quantum random number generation protocol and experimentally demonstrate it. In our protocol, we make no assumptions about the source. Some reasonable assumptions on the trusted two-dimensional measurement are needed, but we do not require a detailed characterization. Even if considering the most general quantum attack and using the general sources, we achieve a randomness generation rate of over 1 Mbps with a universal composable security parameter of 10^{-10}.
Random numbers are used in various domains, including quantum communication and cryptography applications such as key generation and authentication. Quantum mechanics has the intrinsic ability to generate truly random numbers, making it an ideal alternative for scientific applications that require randomness. Quantum wireless communication is proposed as a new means of communication that is safe, secure, and efficient. The simplicity of our source rotation gate, combined with its independently verifiable solitary unpredictability, is essential to obtain quantum random number generators without spending any money. In this chapter, we explore and study the 24-qubit random number. The worst-case entropy value for such randomly produced integers is 0.999445, with the min-entropy of such numbers being 0.0008. Additionally, steering restart tests were used to validate later verification of true randomness, and the statistical characteristics of the True Random Number Generation (TRNG) were assessed using an autocorrelation study and the statistical test suites.