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

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

Entanglement and Teleportation in Bipartite System

We present a mathematical formulation of old teleportation protocol (original teleportation protocol introduced by Bennett et.al.) for mixed states and study in detail the role of mixedness of the two qubit quantum channel in a teleportation protocol. We show that maximally entangled mixed state described by the density matrix of rank-4 will be useful as a two qubit teleportation channel to teleport a single qubit mixed state when the teleportation channel parameter p1 greater than 0.5. Also we discuss the case when p1 less than equal to 0.5.Comment: 16 pages and 5 figures. Accepted in IJQ

Programming with Quantum Communication

This work develops a formal framework for specifying, implementing, and analysing quantum communication protocols. We provide tools for developing simple proofs and analysing programs which involve communication, both via quantum channels and exhibiting the LOCC (local operations, classical communication) paradigm