Abstract
Random numbers are valuable for applications ranging from cryptographic tasks to numerical simulations. Genuine randomness is generally considered possible only with a quantum system described by quantum mechanics. The dimension witness allows us to distinguish between classical and quantum scenarios, and assess the system dimensions from experimental data. Accordingly, a quantum random number generator (QRNG) based on dimension witnesses has attracted intensive study. Here we extend the prepare-and-measure QRNG protocol proposed by Brunner et al. [Phys. Rev. Lett. 112, 140407 (2014).PRLTAO0031-900710.1103/PhysRevLett.112.140407] to a more general and better one. In our protocol, all the mutually unbiased bases of two-dimensional Hilbert space can be used to bound the min-entropy, which leads to a higher random number generation rate in different optical path losses and different environmental disturbances. We also demonstrate a proof-of-principle realization of our protocol, in which the random number rate increases by more photon polarization mutually unbiased bases compared with the previous one. Our method may also be applicable in higher-dimensional quantum systems.
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