Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
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A bipartite quantum interaction corresponds to the most general quantum interaction that can occur between two quantum systems. In this work, we determine bounds on the capacities of bipartite interactions for entanglement generation and secret key agreement. Our upper bound on the entanglement generation capacity of a bipartite quantum interaction is given by a quantity that we introduce here, 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 introduced here also, 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 quantum reading 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 memory cell. Given a set of point-to-point quantum 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 the environment of the channels. We derive both lower and upper bounds on the private reading capacities of a 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.
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