Random numbers have considerable importance in science and technology, gambling, and, most significantly, cryptography. Attempts to achieve unpredictable, independent, and practical quantum random number generator (QRNG) drives scientist to semi device-independent (DI) QRNGs. This type of generator, besides being performant and secure, are easy to be implemented. This paper demonstrates a semi-DI QRNG based on the ambiguity in discriminating non-orthogonal quantum states. Non-orthogonal quantum states can not be perfectly distinguished due to the inevitable uncertainty imposed by the quantum theory. This uncertainty can be exploited, as in this protocol, to generate secure and private random numbers. Additionally, a generalized security estimation based on state overlap and unambiguous state discrimination for multiple inputs and outputs in the form of a semidefinite program (SDP) is presented.

The protocol is tested with a simple experimental setup, capable of realizing two configurations (Config. I and II) for the ternary time-bin encoding scheme. The experimental design is easy to implement and comprises commercially available off-the-shelf (COTS) components at the telecom wavelength (1550), granting a secure and certifiable entropy source. The combination of ease of implementation, scalability, high-security level, and output-entropy make our system a promising candidate for commercial QRNGs.

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