The Logic of Entanglement

We expose the information flow capabilities of pure bipartite entanglement as a theorem — which embodies the exact statement on the ‘seemingly acausal flow of information’ in protocols such as teleportation [14]. We use this theorem to redesign and analyze known protocols (e.g. logic gate teleportation [10] and entanglement swapping [15]) and show how to produce some new ones (e.g. parallel composition of logic gates). We also show how our results extend to the multipartite case and how they indicate that entanglement can be measured in terms of ‘information flow capabilities’. Ultimately, we propose a scheme for automated design of protocols involving measurements, local unitary transformations and classical communication.