Chinese Optics Letters

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Experimental randomness certification with a symmetric informationally complete positive operator-valued measurement

Random numbers are important resources in science, engineering and even economics. Methods based on some deterministic algorithm and some randomness seed in most computers, can produce numbers with random statistic distribution, but be possibly predicted in principle, which is called pseudorandom number generator. However, the true random numbers can be generated from unpredictable physical events, guaranteed by the intrinsic randomness of some physical processes.

Quantum random number generator (QRNG) is based on the inherent randomness of quantum mechanics. The nonlocality of two entangled subsystems provides a good candidate to generate true random numbers independent of the devices. For the standard protocol with two measurement devices and a maximally-entangled two-qubit system, the maximal random number generated via local projective measurements is one bit per round. If non-projective measurement is allowed, the bound can be exceeded. Recently, Andersson et al. proved that a symmetric, informationally complete, positive operator-valued measurement (SIC-POVM) can be used for the certification of two random bits at most.

Fig. 1: Schematic of the experimental setup for randomness certification based on SIC-POVM.

The experiment introduced by Mr. Chenxi Liu from a research group led by Prof. Jian Li and Prof. Qin Wang of Nanjing University of Posts and Telecommunications in Chinese Optics Letters, Volume 18, Issue 10, 2020 (C. Liu, et al., Experimental randomness certification with a symmetric informationally complete positive operator-valued measurement) is a demonstration of randomness generation more than one bit via positive operator-valued measurements (POVM) and maximally-entangled state.

The two-photon in entangled state is generated via spontaneous parametric down-conversion process. The local projective measurements on the polarization states of single photon are realized by wave plates, polarization beam splitters and single photon detectors. A quantum walk setup is built with wave plates and beam displacers to perform the symmetric informationally-complete positive operator-valued measurement, a special non-projective measurement. To ensure the entanglement and corresponding measurements, an elegant Bell inequality is measured in the experiment. The classical bound of the inequality is 4, while the maximum quantum violation is 4\sqrt(3). The experimental result is about 6.7998, close to the quantum bound, which guarantees more than one bit randomness can be generated per round in the experiment.

Prof. Qin Wang from Nanjing University of Posts and Telecommunications believes that the QRNG with quantum nonlocality and non-projective measurement is more efficient. And it can be further certified to be device-independent (DI), where device-independent - random number generator (DI-RNG), as the most secure random number generator, would play an important role in some key areas, such as secure communication.