We investigate the generation of entanglement between two noninteracting systems by synthesizing a quantum process from the superposition of distinct processes characterized by local-only operations. Our analysis leads to the derivation of a universal trade-off relation, $P_{\text{succ}}(1+\mathcal{C})\le 1$, that fundamentally bounds the success probability ($P_{\text{succ}}$) and the generated entanglement (concurrence $\mathcal{C}$). The derivation of this trade-off relation is inspired by indefinite causal order but applies to a broader class of quantum processes. Next, we show that the mathematical structure of this bound predicts the existence of a “quasideterministic” mode of operation, a surprising phenomenon which we then confirm with concrete entanglement generation protocols, where a maximally entangled state is guaranteed to be produced. In this mode of operation, both outcomes of the postselection measurement on the auxiliary control system result in a maximally entangled state of the target system. Furthermore, we demonstrate how this general principle can be realized using a quantum switch, which leverages an indefinite causal order as a physical resource, and explore the rich variety of dynamical behaviors governed by the universal trade-off. Our results establish a general principle for entanglement generation with superposition of quantum processes and introduce a way of controlling entanglement generation.

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• Quantum correlations, foundations & formalism
• Quantum information theory