  The study of memory effects in quantum channels helps in developing
characterization methods for open quantum systems and strategies for quantum
error correction. Two main sets of channels exist, corresponding to system
dynamics with no memory (Markovian) and with memory (non-Markovian).
Interestingly, these sets have a non-convex geometry, allowing one to form a
channel with memory from the addition of memoryless channels and vice-versa.
Here, we experimentally investigate this non-convexity in a photonic setup by
subjecting a single qubit to a convex combination of Markovian and
non-Markovian channels. We use both divisibility and distinguishability as
criteria for the classification of memory effects, with associated measures.
Our results highlight some practical considerations that may need to be taken
into account when using memory criteria to study system dynamics given by the
addition of Markovian and non-Markovian channels in experiments.
