There are processes that cannot generate entanglement but may, nevertheless, amplify entanglement already present in a system. Here, we show that a nonentangling operation can increase the Schmidt number of a quantum state only if it can generate entanglement with some nonzero probability. This is in stark contrast to the case where the parties of a quantum network are only able to control their joint state by local operations and classical communication (LOCC). There, being able to apply operations probabilistically (stochastic LOCC) does not increase the Schmidt number. Our findings show that certain nonentangling operations become entangling when specific measurement outcomes are selected. This naturally leads us to the class of stochastically nonentangling maps, which are those that cannot generate entanglement even probabilistically. Intrigued by this finding, we devise a Schmidt number for quantum channels that quantifies whether a channel can generate entanglement probabilistically. Moreover, we show that a channel is nonentangling if and only if its dual map is witness preserving—it takes entanglement witnesses to witnesses. Based on this finding, we derive inequalities whose violation signals that a process generates entanglement.

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• Quantum correlations in quantum information
• Quantum correlations, foundations & formalism
• Quantum information theory