  Quantum mechanics is known to provide significant improvements in information
processing tasks when compared to classical models. These advantages range from
computational speeds-up to security improvements. A key question is where these
advantages come from. The toy model developed by Spekkens [R. W. Spekkens PRA
75, 032110 (2012)] mimics many of the features of quantum mechanics, such as
entanglement and no-cloning, regarded as being important in this regard,
despite being a local hidden variable theory. In this work we study several
protocols within Spekkens' toy model where we see it can also mimic the
advantages and limitations shown in the quantum case. We first provide explicit
proofs for the impossibility of toy bit-commitment and the existence of a toy
error correction protocol and consequent $k-$threshold secret sharing. Then,
defining a toy computational model based on the quantum one-way computer we
prove the existence of blind and verified protocols. Importantly, these two
last quantum protocols are known to achieve a better-than-classical security.
Our results suggest that such quantum improvements need not arise from any
Bell-type non locality or contextuality, but rather as a consequence of
steering correlations.
