Squeezed‐State Semi‐Device‐Independent Quantum Randomness Generation
Hamid Tebyanian · Advanced Quantum Technologies · 2026
ABSTRACT This paper investigates semi‐device‐independent quantum randomness generation with a trusted binary pure‐state source and an untrusted binary detector whose side information is classical. We derive a closed‐form Shannon‐rate expression, depending only on the trusted Gram overlap of the two source states and the observed symmetric error probability. The full binary‐qubit positive operator‐valued measure (POVM) optimization must include the two deterministic extreme points omitted by the projective‐only treatment; including them gives a substantially lower, and correct, certified rate. The closed form is an unconditional upper bound on the certified asymptotic independent and identically distributed (i.i.d.) Shannon rate, and becomes tight on a numerically verified dual‐feasibility region; it is the certified rate only inside this region; values beyond it are bounded numerically. We then apply the result to squeezed‐coherent binary phase‐shift keying (BPSK) sources, showing how squeezing changes the trade‐off between state distinguishability and certified randomness in the lossless and lossy regimes. At fixed mean photon number and squeezing, the certified rate is largest when the displacement lies along the anti‐squeezed quadrature, and we obtain the corresponding limiting value. An adversary holding a detector‐purification register that tags the outcome lies outside the classical‐side‐information model and would reduce the certified rate to zero.