A bipartite quantum interaction corresponds to the most general quantum
interaction that can occur between two quantum systems in the presence of a
bath. In this work, we determine bounds on the capacities of bipartite
interactions for entanglement generation and secret key agreement between two
quantum systems. Our upper bound on the entanglement generation capacity of a
bipartite quantum interaction is given by a quantity called the bidirectional
max-Rains information. Our upper bound on the secret-key-agreement capacity of
a bipartite quantum interaction is given by a related quantity called the
bidirectional max-relative entropy of entanglement. We also derive tighter
upper bounds on the capacities of bipartite interactions obeying certain
symmetries. Observing that reading of a memory device is a particular kind of
bipartite quantum interaction, we leverage our bounds from the bidirectional
setting to deliver bounds on the capacity of a task that we introduce, called
private reading of a wiretap memory cell. Given a set of point-to-point quantum
wiretap channels, the goal of private reading is for an encoder to form
codewords from these channels, in order to establish secret key with a party
who controls one input and one output of the channels, while a passive
eavesdropper has access to one output of the channels. We derive both lower and
upper bounds on the private reading capacities of a wiretap memory cell. We
then extend these results to determine achievable rates for the generation of
entanglement between two distant parties who have coherent access to a
controlled point-to-point channel, which is a particular kind of bipartite
interaction.Comment: v3: 34 pages, 3 figures, accepted for publication in Physical Review
