I was going through the proof of security of the modified Lo-Chau protocol, which eventually leads to the proof of security of BB84. In the error correction step, Nielson-Chuang mention that any bipartite state $\rho^{AB}$, with the promise that there are at most $t$ Pauli errors on the system $B$, can be corrected by measuring $g_i\otimes g_i$, where $g_i$ ranges over the set of generators $\langle g_1, g_2, \ldots, g_{n-m}\rangle$. When I say corrected I mean that they can distill the $m$ EPR states $|\Phi\rangle^{\otimes m}$. Of course Alice and Bob have to do this by measuring $g_i$ locally and then using classical communication. My question is, is there a proof of this claim? Nielson-Chaung provide an exercise, Exercise 12.34, but I am having a hard time with this. Any help is appreciated.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.