Abstract
Quantum cryptographic protocols solve the longstanding problem of distributing a shared secret string to two distant users by typically making use of one-way quantum channel. However, alternative protocols exploiting two-way quantum channel have been proposed for the same goal and with potential advantages. Here, we overview a security proof for two-way quantum key distribution protocols, against the most general eavesdropping attack, that utilize an entropic uncertainty relation. Then, by resorting to the “smooth” version of involved entropies, we extend such a proof to the case of finite key size. The results will be compared to those available for one-way protocols showing some advantages.
Highlights
Two-way quantum key distribution (QKD) schemes have evolved from a theoretic framework in the context of deterministic schemes to experimental realizations for QKD purposes [1]
Following [9], in the case for the LM05, we can use the bits derived in the control mode (CM) to provide for an estimation of the errors in the application of the uncertainty relation using a similar gedankenexperiment where all rounds are CM; and since Bob can choose to measure for encoding mode (EM), security follows from the notion that the better Alice could estimate Bob’s bits in CM, the worse would Eve’s estimation of Bob’s bits in EM
By conventional we refer to the BB84 in its original form where the choice of bases is equiprobable, resulting in only half of qubits transmitted could be used as a raw key
Summary
Two-way quantum key distribution (QKD) schemes have evolved from a theoretic framework in the context of deterministic schemes to experimental realizations for QKD purposes [1]. Entropy 2015, 17 traveling to and fro between the legitimate parties This naturally makes use of the quantum channel twice. A very important fact that sets constraints within the operational context would be the issue of how such proofs are based on asymptotic analysis that holds true only for infinitely long keys; the concern regarding the security nature of realistic keys, which are finitely long, becomes evident. This has spurred a number of studies including [7,8,9]. These will be compared to an asymmetrical BB84; essentially a BB84 protocol with one basis preferred over another mainly for a more efficient scenario compared to a standard BB84 where choices of bases are equiprobable [8,10]
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