Multi-time quantum processes are endowed with the same richness as multipartite states, including temporal entanglement and exotic causal structures. However, experimentally probing these rich phenomena leans heavily on fast and clean mid-circuit measurements, which are rarely available. We show here how surprisingly accessible these phenomena are in nascent quantum processors even when faced with substantially limited control. We work within the limitation where only unitary control is allowed, followed by a terminating measurement. Within this setting, we first develop a witness for genuine multi-time entanglement, and then methods to bound (from top and bottom) multi-time entanglement, non-Markovianity, purity, entropy, and other correlative measures. Our tools are designed to be implemented on quantum information processors, which we proceed to demonstrate. Finally, we discuss the limitations of these methods by testing them across random multi-time processes. Conceptually, this broadens our understanding of the extent to which temporal correlations may be determined with only deterministic control. Our techniques are pertinent to generic quantum stochastic dynamical processes, with a scope ranging across condensed matter physics, quantum biology, and in-depth diagnostics of NISQ-era quantum devices.
