The paper by Samson Abramsky and Bob Coecke introduces a novel approach to quantum information and computation by recasting the standard axiomatic presentation of quantum mechanics in terms of compact closed categories with biproducts. This abstract framework captures essential structures found in key quantum information protocols, such as teleportation, logic-gate teleportation, and entanglement swapping. The authors demonstrate how the structures of compact closure and biproducts naturally emerge 'scalars' and a 'Born rule', providing a new perspective on quantum systems. The abstract setting allows for precise formulations and proofs of the correctness of these protocols, capturing both the information-flow aspect and the branching due to quantum indeterminism. The paper also explores the generality and axiomatic freedom of the approach, showing how it can be applied to different models and protocols, and provides detailed formal descriptions and proofs for the example protocols.The paper by Samson Abramsky and Bob Coecke introduces a novel approach to quantum information and computation by recasting the standard axiomatic presentation of quantum mechanics in terms of compact closed categories with biproducts. This abstract framework captures essential structures found in key quantum information protocols, such as teleportation, logic-gate teleportation, and entanglement swapping. The authors demonstrate how the structures of compact closure and biproducts naturally emerge 'scalars' and a 'Born rule', providing a new perspective on quantum systems. The abstract setting allows for precise formulations and proofs of the correctness of these protocols, capturing both the information-flow aspect and the branching due to quantum indeterminism. The paper also explores the generality and axiomatic freedom of the approach, showing how it can be applied to different models and protocols, and provides detailed formal descriptions and proofs for the example protocols.