Distinguishing quantum processes with bounded coherent memory

Distinguishing multi-time quantum processes is a fundamental task underlying the diagnosis, benchmarking, and learning of temporally correlated quantum dynamics. The standard benchmark for distinguishing two processes is the strategy-norm distance, which optimizes over arbitrary adaptive probing strategies but can require large coherent memory and time-dependent control. We introduce machines for autonomous distinction $mathsf{MAD}$s: probing strategies that apply the same quantum instrument at each time step, retain the full classical outcome record, and carry a coherent memory of dimension d_A. Optimizing over these strategies defines a memory-parametrized distinguishability measure, d^(N)_{mathsf{MAD}}\(mathbf{P}^N,mathbf{Q}^N;d_A\). We show that the resulting hierarchy is monotone in coherent memory and complete at finite times. Specifically, any admissible N-step probing strategy can be compiled into a single mathsf{MAD} with an internal counter and sufficiently large coherent memory, so the hierarchy saturates the strategy-norm benchmark. For recurrent processes generated by repeated system--environment interactions, we derive a single-step description that separates the generation of new distinguishing information from the propagation and decay of information generated at earlier times. Numerical results in a repeated-interaction model show that increasing coherent memory systematically improves the mathsf{MAD} success probability and closes the gap to the strategy-norm distance while remaining substantially more tractable to evaluate. mathsf{MAD} distinguishability therefore provides an operational and scalable framework for quantifying what can be learned about genuinely multi-time quantum processes with bounded coherent memory.