Abstract
A commonly held tenet is that lasers well above threshold emit photons in a coherent state, which follow Poissonian statistics when measured in photon number. This feature is often exploited to build quantum-based random number generators or to derive the secure key rate of quantum key distribution systems. Hence the photon number distribution of the light source can directly impact the randomness and the security distilled from such devices. Here, we propose a method based on measuring correlation functions to experimentally characterize a light source's photon statistics and use it in the estimation of a quantum key distribution system's key rate. This promises to be a useful tool for the certification of quantum-related technologies.
Highlights
Quantum random number generators (QRNGs) [1,2,3] and quantum key distribution (QKD) [4,5,6] are the first quantum-related technology to leap out of the lab and reach the maturity necessary for the market.The goal of a QRNG is to generate unpredictable numbers based on the laws of quantum physics
As for QRNGs based on the phase noise of a laser [13,14,15,16,17,18], the Poissonian nature of the source can evidence the good functioning of the randomness-generating mechanism
We are interested in the characterisation of the photon statistics pn of a light source that is suitable for quantum-related technologies like a QRNG or a QKD system
Summary
Quantum random number generators (QRNGs) [1,2,3] and quantum key distribution (QKD) [4,5,6] are the first quantum-related technology to leap out of the lab and reach the maturity necessary for the market. The case (b) is the least secure, because the photon bunching effect favours the redundant encoding of the information This shows that even if the mean photon number μ is well characterised, the photon number distribution probability pn can still determine the insecurity of a QKD system. One method would be to use photon number resolving detectors or, equivalently, space-multiplexed or time-multiplexed threshold detectors [21] In this case, a precise calibration of the detection efficiency would be required, which is far from trivial. Experimentally it is not possible to measure the correlation functions to all orders, we will show that measuring them up to the fourth order is sufficient to determine tight bounds on the secure key rate of a QKD system To apply this method, we will work in the low detection efficiency approximation. IV we will exploit our experimental results to estimate the secure key rate of a QKD system [26]
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