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.
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