Extend certified randomness results to infinite-dimensional systems

Extend the certified lower bounds on extractable randomness for the energy-constrained semi-device-independent prepare-and-measure scenario with shared entanglement from arbitrarily large finite-dimensional quantum systems to infinite-dimensional systems, as relevant for photonic implementations.

Background

The paper’s dimension-independent relaxation provides security guarantees for every finite source dimension and imposes no dimension bound on the measurement or adversary systems, but it does not establish the result for genuinely infinite-dimensional Hilbert spaces. Such systems are particularly relevant to photonic implementations, where optical modes naturally have unbounded dimension. The authors therefore explicitly leave the infinite-dimensional extension unresolved.