Encyclopedia
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.
- quantum random number
- vacuum state
- maximization of quantum conditional min-entropy
1. Introduction
Randomness is one vital ingredient in modern information science, in the regime of both classical and quantum [1, 2], since encryption is founded upon the trust in random numbers [3-5]. The demand for true and unique randomness in these applications has triggered various proposals for producing random numbers based on the measurements of quantum observables, which offer the verifiability and ultimate in randomness. In the past two decades, there has been tremendous development for various types of quantum RNG [6-15]. Among these proposals, random number generation based on homodyne measurement of quantum vacuum state is especially appealing in practice since highly efficient photodiodes working at room temperature can be applied [11]. Vacuum state is a pure quantum state with the lowest energy and independent of any external physical quantities. It cannot be correlated or controlled by an attacker, therefore unique random numbers can be yielded by measuring the quadrature amplitude of the vacuum state [16, 17]. All the components in this scheme, including laser source, beam splitter and photo detectors have been integrated on a single chip recently [18]. Meanwhile, bit conversion and post-processing are easy to be implemented in virtual “hardware” inside the field-programmable gate array (FPGA). Chip-size integration of the QRNG is expectable. Several dedicated researches have been developed to enhance the generation rate of random bits in this proposal, such as schemes based on optimization of the digitization algorithm [19], implementation of fast randomness extraction in the post-processing [20], application of squeezing vacuum state to increase entropy in raw data [21], and optimization of ADC parameters to improve the quantum entropy in the raw data [22]. In this paper, considering the effects of the classical noise, we discuss the role of homodyne gain in enhancing quantum entropy in the vacuum-based quantum RNG working in the optimum dynamical ADC range scenario. Conditional min-entropy is applied to critically assess the quantum entropy in the quantum RNG. It is the key input parameter of randomness extractor and determines the extraction ratio of true randomness from the raw random sequence, thereby affects the generation speed of quantum RNG significantly.
2. Quantum entropy evaluation and enhancing in vacuum-based quantum RNG
