In two model scenarios, the non-Markovian memory induced by the quantum SWITCH vanishes when an inert extension is included, so it is not genuine quantum non-Markovianity.
Hardy, Towards quantum gravity: a framework for prob- abilistic theories with non-fixed causal structure, Journal of Physics A: Mathematical and Theoretical40, 3081 (2007)
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Quantum SWITCH-induced non-Markovianity is not entirely quantum
In two model scenarios, the non-Markovian memory induced by the quantum SWITCH vanishes when an inert extension is included, so it is not genuine quantum non-Markovianity.