True randomness from an incoherent source

Abstract

Quantum random number generators (QRNGs) harness the intrinsic randomness in measurement processes: the measurement outputs are truly random given the input state is a superposition of the eigenstates of the measurement operators. In the case of trusted devices, true randomness could be generated from a mixed state ρ so long as the system entangled with ρ is well protected. We propose a random number generation scheme based on measuring the quadrature fluctuations of a single mode thermal state using an optical homodyne detector. By mixing the output of a broadband amplified spontaneous emission (ASE) source with a single mode local oscillator (LO) at a beam splitter and performing differential photo-detection, we can selectively detect the quadrature fluctuation of a single mode output of the ASE source, thanks to the filtering function of the LO. Experimentally, a quadrature variance about three orders of magnitude larger than the vacuum noise has been observed, suggesting this scheme can tolerate much higher detector noise in comparison with QRNGs based on measuring the vacuum noise. The high quality of this entropy source is evidenced by the small correlation coefficients of the acquired data. A Toeplitz hashing extractor is applied to generate unbiased random bits from the Gaussian distributed raw data, achieving an efficiency of 5.12 bits per sample. The output of the Toeplitz extractor successfully passes all the NIST statistical tests for random numbers. Truly random numbers are required in many branches of science and technology, from fundamental research in quantum mechanics [1] to practical applications such as cryptography [2]. While a pseudorandom number generator can expand a short random seed into a long train of apparent "random" bits using deterministic algorithms, the entropy of generated random numbers is still bounded by the original short random seed. To generate true randomness, researchers have been exploring various physical processes.Quantum random number generation is an emerging technology [3,4], which can provide high-quality random numbers with proven randomness. Different from physical random number generators exploring chaotic behaviors of classical systems, a quantum random number generator (QRNG) harnesses the truly probabilistic nature of fundamental quantum processes [5,6].In general, the process of random number generation can be divided into two steps: the measurement step and the randomness extraction step. In the first * qib1@ornl.gov a

Experimental study of a quantum random-number generator based on two independent lasers

“…Therefore, we conclude that case II, cw+pulse, may be the best choice for high-speed implementation of QRNG based on quantum phase noise (as demonstrated recently in [23,24]), while case I is suitable for simple and lowcost applications that may require slow rate QRNG only. Notice that high-speed implementation of case I is still possible by changing the scheme to a broadband source and a homodyne detection [25].…”

Eavesdropping attack on a trusted continuous-variable quantum random-number generator

“…This result has immediate implications for QRNGs based on continuous variables. QRNGs based on thermal light have been shown to offer enhanced min-entropy compared to QRNGs sampling vacuum, when using the same experimental resolution [30], but they either need to be operated as trusted QRNGs or used in applications where security of the random numbers is not relevant. Otherwise, eavesdropping attacks may reduce the performance of the thermal light QRNG such, that it does not offer any advantages compared to sampling vacuum.…”

“…In the following, we will denote the binned quadratures as X and P . Such QRNGs have already been realized using the vacuum [33] or thermal light [30] as input states. The random numbers determined this way are usually not distributed uniformly, so it is possible to perform additional randomness extraction [34] to create a compressed shorter string composed of independent identically distributed random numbers.…”

Passive state preparation in continuous-variable quantum key distribution

“…It is a common practice to apply a quantum random number generator (QRNG) [38,39] in prepare-and-measure QKD for state prepara- tion and/or measurement basis selection. As we have discussed in [34], while quantum randomness is ultimately connected to quantum superposition states, in the fully trusted device scenario, the quantum state received by the detector does not need to be a pure state. One illustrative example is the first generation QRNG, where electrons from a radioactive source such as 90 Sr are detected by a Geiger Mueller tube at random times [40,41].…”

“…2) with vacuum state input is employed as a broadband thermal source. Previous studies have shown that the ASE noise generated by a fiber amplifier is thermal [22,[32][33][34]. To select out a single polarization mode, a fiber pigtailed polarizer (Pol in Fig.…”