Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 53 / 4 / A / 3 / Solution

No secure key can be produced from this state alone. Factoring the printed amplitudes gives the normalized product stateEve is uncorrelated with the joint pure state, but Alice and Bob also have no correlations with each other: local outcome probabilities factor. They may generate independent private random bits locally, but local operations and classical communication cannot make those bits shared and secret using only public messages. A product state supplies no shared secret resource.