Estimating security of the quantum key distribution from the guesswork

Quantum key distribution can provide information-theoretic security keys. In practice, the eavesdropper may attack the transmitted quantum state, which makes some information leakage to the generated key. The security of the final key depends on how difficult it is for the eavesdropper to guess the key. The guessing probability is bounded by the trace distance between the practical generated quantum state and the ideal quantum state and hence can be applied to estimate security of quantum key distribution. With the trace distance s and the secret key length n, we prove that the guessing probability can reach the upper bound epsilon +2(-n) in some special cases. We show that different attacking strategies will give different numbers of guesses, sometimes even completely subversive differences, to get the final key. Our results demonstrate that the appropriate security parameter epsilon should be carefully selected to guarantee the security of the generated key.

Automated summary

Quantum key distribution provides information-theoretic security keys. The security of the generated key depends on the difficulty for the eavesdropper to guess the key and the distance between the practical and ideal quantum states. Selecting appropriate security parameters ensures the security of the generated key.