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Semi-device independent (Semi-DI) quantum random number generators (QRNG)gained attention for security applications, offering an excellent trade-offbetween security and generation rate. This paper presents a proof-of-principletime-bin encoding semi-DI QRNG experiments based on a prepare-and-measurescheme. The protocol requires two simple assumptions and a measurablecondition: an upper-bound on the prepared pulses' energy. We lower-bound theconditional min-entropy from the energy-bound and the input-output correlation,determining the amount of genuine randomness that can be certified. Moreover,we present a generalized optimization problem for bounding the min-entropy inthe case of multiple-input and outcomes in the form of a semidefinite program(SDP). The protocol is tested with a simple experimental setup, capable ofrealizing two configurations for the ternary time-bin encoding scheme. Theexperimental setup is easy-to-implement and comprises commercially availableoff-the-shelf (COTS) components at the telecom wavelength, granting a secureand certifiable entropy source. The combination of ease-of-implementation,scalability, high-security level, and output-entropy make our system apromising candidate for commercial QRNGs.

Practical Semi-Device Independent Randomness Generation Based on Quantum State's Indistinguishability