  In single-particle entanglement (SPE) two degrees of freedom of a single
particle are entangled. SPE is a resource that can be exploited both in quantum
communication protocols and in experimental tests of noncontextuality based on
the Kochen-Specker theorem. SPE can be certified via a Bell test. Experiments
of Bell inequality violation by single particle entangled systems may be
affected by an analogue of the locality loophole in this context, due to the
presence of unavoidable non-idealities in the experimental devices which
actually produce unwanted correlations between the two observables that are
simultaneously measured. This issue is tackled here by quantitatively analyzing
the behaviour of realistic devices in SPE experiments with photons. In
particular, we show how it is possible to provide a semi-device independent
randomness certification of realistic quantum random number generators based on
Bell inequality violation by SPE states of photons. The analysis is further
enlarged to encompass, with a Markovian model, memory effects due to dead time,
dark counts and afterpulsing affecting single photon detectors, in particular
when not dealing with coincidence measurements. An unbiased estimator is also
proposed for quantum transition probabilities out of the collection of
experimental data.
