Quantum SWITCH-induced non-Markovianity is not entirely quantum

Indefinite causal order, realized through the quantum SWITCH, allows quantum channels to act in a coherent superposition of sequences. While this framework provides operational advantages in computation and communication, the physical origin of these benefits remains debated. Recent research has suggested that the quantum SWITCH generates non-Markovian memory effects—specifically information backflow—which might be the source of its performance gains. This paper investigates whether these memory effects are genuinely quantum or if they arise from classical origins.

To distinguish between genuine quantum non-Markovianity and classical memory, the authors employ the framework of non-causal information revivals. They analyze two representative scenarios: discrete-time evolution and dynamical maps in open quantum systems. The researchers monitor the quantum mutual information (QMI) between a system and an isolated reference. They test whether the observed revivals in mutual information persist when the system is extended by an inert ancilla. If the apparent memory effects vanish upon conditioning on an extended system, they are classified as non-genuine (classical) rather than genuinely quantum.

Through a systematic analysis of both discrete and continuous dynamical processes, the authors demonstrate that the memory effects induced by the quantum SWITCH do not constitute genuine quantum non-Markovianity. Although the SWITCH-based dynamics exhibit clear signatures of non-Markovianity—such as temporary increases in mutual information—these revivals disappear when the environment is properly extended. This indicates that the observed information backflow is a consequence of classical correlations rather than intrinsic quantum memory. Consequently, the authors suggest that the operational advantages of indefinite causal order cannot be attributed to genuine quantum non-Markovianity.