A bipartite quantum interaction corresponds to the most general quantuminteraction that can occur between two quantum systems. In this work, wedetermine bounds on the capacities of bipartite interactions for entanglementgeneration and secret key agreement. Our upper bound on the entanglementgeneration capacity of a bipartite quantum interaction is given by a quantitythat we introduce here, called the bidirectional max-Rains information. Ourupper bound on the secret-key-agreement capacity of a bipartite quantuminteraction is given by a related quantity introduced here also, called thebidirectional max-relative entropy of entanglement. We also derive tighterupper bounds on the capacities of bipartite interactions obeying certainsymmetries. Observing that quantum reading is a particular kind of bipartitequantum interaction, we leverage our bounds from the bidirectional setting todeliver bounds on the capacity of a task that we introduce, called privatereading of a memory cell. Given a set of point-to-point quantum channels, thegoal of private reading is for an encoder to form codewords from thesechannels, in order to establish secret key with a party who controls one inputand one output of the channels, while a passive eavesdropper has access to theenvironment of the channels. We derive both lower and upper bounds on theprivate reading capacities of a memory cell. We then extend these results todetermine achievable rates for the generation of entanglement between twodistant parties who have coherent access to a controlled point-to-pointchannel, which is a particular kind of bipartite interaction.
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