Recently, semi-device-independent protocols have attracted increasing attention, guaranteeing security with few hypotheses and experimental simplicity. In this paper, we demonstrate a many-outcome scheme with binary phase-shift keying (BPSK) for a semi-device-independent protocol based on the energy assumption. We show in theory that the number of certified random bits of the $d$-outcome system outperforms the standard scheme (binary outcomes). Furthermore, we compare the results of two well-known measurement schemes, homodyne detection and heterodyne detection. Taking into account the experimental imperfections, we discuss the experimental feasibility of the $d$-outcome design, and finally, we experimentally validate this approach with an experiment based on BPSK modulation and heterodyne detection.

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• Quantum cryptography
• Quantum information processing with continuous variables