To guarantee the security of uniform random numbers generated by a quantum random-number generator, we study secure extraction of uniform random numbers when the environment of a given quantum state is controlled by the third party, the eavesdropper. Here we restrict our operations to incoherent strategies that are composed of the measurement on the computational basis and incoherent operations (or incoherence-preserving operations). We show that the maximum secure extraction rate is equal to the relative entropy of coherence. By contrast, the coherence of formation gives the extraction rate when a certain constraint is imposed on the eavesdropper's operations. The condition under which the two extraction rates coincide is then determined. Furthermore, we find that the exponential decreasing rate of the leaked information is characterized by R\'enyi relative entropies of coherence. These results clarify the power of incoherent strategies in random-number generation, and can be applied to guarantee the quality of random numbers generated by a quantum random-number generator.
To guarantee the security of uniform random numbers generated by a quantum random-number generator, we study secure extraction of uniform random numbers when the environment of a given quantum state is controlled by the third party, the eavesdropper. Here we restrict our operations to incoherent strategies that are composed of the measurement on the computational basis and incoherent operations (or incoherence-preserving operations). We show that the maximum secure extraction rate is equal to the relative entropy of coherence. By contrast, the coherence of formation gives the extraction rate when a certain constraint is imposed on the eavesdropper's operations. The condition under which the two extraction rates coincide is then determined. Furthermore, we find that the exponential decreasing rate of the leaked information is characterized by R'enyi relative entropies of coherence. These results clarify the power of incoherent strategies in random-number generation, and can be applied to guarantee the quality of random numbers generated by a quantum random-number generator.
How much cryptographically-secure randomness can be extracted from a quantum state? This fundamental question probes the absolute limits of quantum random number generation (QRNG) and yet, despite the technological maturity of QRNGs, it remains unsolved. In this work we consider a general adversarial model that allows for an adversary who has quantum side-information about both the source and the measurement device. Using links between randomness extraction rates and sandwiched Rényi entropies, we provide compact, easy to compute, achievable rates of secure randomness extraction from quantum states. In turn, this provides a simple to evaluate benchmarking tool for the randomness generation rates of QRNG protocols.
Quantum coherence serves as a fundamental resource for generating intrinsic randomness, yet the quantification of randomness in quantum random number generators (QRNGs) based on spontaneous emission has remained largely phenomenological. Existing randomness analysis lacks rigorous adversarial models and a clear characterization of the role of quantum coherence in these systems. In this work, we develop a comprehensive quantum information-theoretic framework for randomness generation in spontaneous emission processes. We characterize two distinct eavesdropping strategies: one where the adversary directly accesses the atom ensemble, and the other where the adversary accesses only its purification. Our analysis reveals that when randomness is generated through single-photon detection and temporal mode measurements, the QRNG is vulnerable to the first adversary scenario, though it still guarantees a lower bound on intrinsic randomness against the second adversary scenario even under maximal information leakage from the atoms. In contrast, QRNGs based on spatial mode detection and phase fluctuations demonstrate security against both types of adversaries, providing robust randomness generation. Furthermore, we provide a quantitative calculation of intrinsic randomness for these spontaneous-emission-based QRNG schemes.
Random numbers generated via quantum process is indeterministic, which are of essential to the cryptographic communication and the large-scale computer modeling. However, in realistic scenarios, classical noises can inevitably contaminate the raw sequences of a quantum randomness number generator (QRNG), and then compromise the security of the QRNG. Min-entropy is a useful approach that can quantify the randomness independent of side-information. To enhance the extractable randomness of the raw sequences arising from the QRNG, we propose a new method which exploits non-uniform quantization methods instead of uniform sampling methods and effectively enhances the extractable randomness from the QRNG at a high quantum-to-classical-noise ratio (QCNR). Given a QCNR as 50 dB and a 16-bit analog-to-digital converter (ADC), the worst-case conditional min-entropy of the non-uniform quantization scheme is improved by nearly 11% compared with that of the uniform sampling scheme.
Randomness is widely used in various fields, including encryption, statistical analysis, and numerical simulations. Randomness is also a fundamental resource in science and engineering. For such applications, we usually need to provide unbiased and independent random bits. This raises the issue of where to get these supposed random bits. Quantum random number generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. In practice, unfortunately, quantum randomness is inevitably mixed with classical randomness due to classical noise. Also, randomness is often correlated and biased. It is necessary to process the resulting raw bits sequence and convert them to good-quality output values that are as close to uniform distribution as possible. Random extractors are required for this. We analyze the randomness obtained by quantum random number generators as well as various examples of post-processing. We discuss the types of randomness extractors. Also, we use information-theoretically secure extractors and present improved novel randomness extraction.
Information-theoretically provable unique true random numbers, which cannot be correlated or controlled by an attacker, can be generated based on quantum measurement of vacuum state and universal-hashing randomness extraction. Quantum entropy in the measurements decides the quality and security of the random number generator (RNG). At the same time, it directly determines the extraction ratio of true randomness from the raw data, in other words, it obviously affects quantum random bits generating rate. In this work, we commit to enhancing quantum entropy content in the vacuum noise based quantum RNG. We have taken into account main factors in this proposal to establish the theoretical model of quantum entropy content, including the effects of classical noise, the optimum dynamical analog-digital convertor (ADC) range, the local gain and the electronic gain of the homodyne system. We demonstrate that by amplifying the vacuum quantum noise, abundant quantum entropy is extractable in the step of post-processing even classical noise excursion, which may be deliberately induced by an eavesdropper, is large. Based on the discussion and the fact that the bandwidth of quantum vacuum noise is infinite, we propose large dynamical range and moderate TIA gain to pursue higher local oscillator (LO) amplification of vacuum quadrature and broader detection bandwidth in homodyne system. High true randomness extraction ratio together with high sampling rate is attainable. Experimentally, an extraction ratio of true randomness of 85.3% is achieved by finite enhancement of the laser power of the LO when classical noise excursions of the raw data is obvious.
Sequences of random numbers are crucial resources for computer simulation and cryptocommunication. Appropriate measurements of the quadratures of a laser's field have been shown to enable efficient generation of high-security, unbiased, truly random numbers. The authors extend this technique to realize a real-time quantum random-number generator, where the source of entropy does not need to be trusted and can be controlled by a malicious third party. By measuring a pair of conjugate quadratures, secure random numbers useful for cryptocommunication can be extracted. The technique is tested on different entropy sources, including thermal and squeezed states of light.