Quantum source-channel coding and non-commutative graph theory

Understand

Alice and Bob receive a bipartite state (possibly entangled) from some finite collection or from some subspace.

• Alice sends a message to Bob through a noisy quantum channel such that Bob may determine the initial state, with zero chance of error.
• This framework encompasses, for example, teleportation, dense coding, entanglement assisted quantum channel capacity, and one-way communication complexity of function evaluation.
• With classical sources and channels, this problem can be analyzed using graph homomorphisms.