Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices

TL;DR

This paper establishes bounds on the capacities for entanglement and secret key agreement in bipartite quantum interactions, introduces the concept of private reading of memory devices, and applies these bounds to quantum communication scenarios.

Contribution

It introduces new capacity bounds for bipartite quantum interactions and applies them to private reading of memory devices, advancing quantum communication theory.

Findings

Upper bounds on entanglement generation capacity using bidirectional max-Rains information.

Upper bounds on secret key capacity via bidirectional max-relative entropy of entanglement.

Derived capacity bounds for private reading of wiretap memory cells.

Abstract

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.