Guessing probability in quantum key distribution

On the basis of the existing trace distance result, we present a simple and efficient method to tighten the upper bound of the guessing probability. The guessing probability of the final key k can be upper bounded by the guessing probability of another key $${\bf{k}}^{\prime}$$, if $${\bf{k}}^{\prime}$$ can be mapped from the final key k. Compared with the known methods, our result is more tightened by thousands of orders of magnitude. For example, given a 10−9-secure key from the sifted key, the upper bound of the guessing probability obtained using our method is 2 × 10−3277. This value is smaller than the existing result 10−9 by more than 3000 orders of magnitude. Our result shows that from the perspective of guessing probability, the performance of the existing trace distance security is actually much better than what was assumed in the past.