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--- projects:physics:qt5104:start [9 days ago ( 4 March 2025)] – [Security and robustness] justin
+++ projects:physics:qt5104:start [9 days ago ( 4 March 2025)] (current) – [BBM-92 QKD security proof] justin
@@ Line 33: / Line 33: @@
 Parameter estimation involves calculating the Hamming distance i.e. $$\sum_{i\in\Pi} \mathbf{1}\{v_i\neq{}w_i\} / k \le\delta$$ and abort if larger than $$\delta$$. More bookkeeping with an additional register that stores $$\phi$$ symbol if the test passes, or $$\perp$$ if test fails.
-Error correction is mostly a classical information theory thing. In a basic description, Alice shares a error syndrome of size $$r$$ with Bob, whom then distills a approximate $$\hat{X}$$. It can be shown that $$r \approx n\delta$$. The result of which is then mapped to $$T$$ and $$T'$$ respectively for Alice and Bob, using the hash function $$H_\text{ec}$$ which is used for checking the error correction was successful. More bookkeeping with flag register to verify $$T=T'$$.
+Error correction is mostly a classical information theory thing. In a basic description, Alice shares a error syndrome of size $$r$$ with Bob, whom then distills a approximate $$\hat{X}$$. It can be shown that $$r \approx nh(\delta)$$. The result of which is then mapped to $$T$$ and $$T'$$ respectively for Alice and Bob, using the hash function $$H_\text{ec}$$ which is used for checking the error correction was successful. More bookkeeping with flag register to verify $$T=T'$$.
   * Associated lemma where the probability of $$X\neq\hat{X}$$ in cases where $$F^\text{ec}=\phi$$, can be bounded above by $$2^{-t}$$.