The concept of correlated measurement outcomes and entanglement is central to quantum key exchange, and therefore the ability to successfully perform entanglement distillation to obtain maximally entangled states is essential for quantum cryptography.
If an entangled pair of particles is shared between two parties, anyone intercepting either particle will alter the overall system, allowing their presence (and the amount of information they have gained) to be determined so long as the particles are in a maximally entangled state. Also, in order to share a secret key string, Alice and Bob must perform the techniques of privacy amplification and information reconciliation to distill a shared secret key string. Information reconciliation is error-correction over a public channel which reconciles errors between the correlated random classical bit strings shared by Alice and Bob while limiting the knowledge that a possible eavesdropper Eve can have about the shared keys. After information reconciliation is used to reconcile possible errors between the shared keys that Alice and Bob possess and limit the possible information Eve could have gained, the technique of privacy amplification is used to distill a smaller subset of bits maximizing Eve's uncertainty about the key.
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