New protocols for quantum key distribution with explicit upper and lower bound on secret key rate

TL;DR

This work tackles practical QKD by introducing two protocols that dispense with entanglement and ideal single-photon sources, enabling implementation with commercially available light sources. Using a bi-directional channel and reduced classical information leakage, the authors derive explicit upper and lower bounds on the secret-key rate under collective attacks, showing that classical pre-processing can raise the tolerable QBER from around $3.14\%$ to about $6.17\%$ (and up to $15\%$ in one variant for S_B2) while maintaining secure key generation. The protocols exhibit higher efficiency than SARG04 under certain conditions (e.g., efficiencies $0.192$ and $0.2069$ for Protocol 2 and Protocol 1, respectively) and offer improved resilience to PNS-type attacks, with critical distances extending beyond BB84 in the scenarios analyzed. The security analysis leverages depolarizing-channel models and information-theoretic bounds to quantify both lower and upper key-rate limits, demonstrating practical relevance for real-world QKD deployments. Overall, the paper contributes explicit, implementable QKD schemes with rigorous statistical-security bounds and a clear evaluation against known attack strategies.

Abstract

We present two new schemes for quantum key distribution (QKD) that neither require entanglement nor an ideal single-photon source, making them implementable with commercially available single-photon sources. These protocols are shown to be secure against multiple attacks, including intercept-resend and a class of collective attacks. We derive bounds on the key rate and demonstrate that a specific type of classical pre-processing can increase the tolerable error limit. A trade-off between quantum resources and information revealed to an eavesdropper (Eve) is observed, with higher efficiency achievable through the use of additional quantum resources. Specifically, our proposed protocols outperform the SARG04 protocol in terms of efficiency at the cost of more quantum resources.

Figures (3)

• Figure 1: (Color online) Plot of the secret key rate as a function of quantum bit error rate $\mathcal{E}$: $(a)$ solid (black) line and dashed (blue) line illustrate the maximum tolerable error limit (security threshold) evaluation for the sequence $S_{B1}$ with and without the introduction of the new variable $\mathcal{Y}$, respectively, $(b)$ plot evaluates the maximum tolerable error limit (security threshold) for the sequence $S_{B2}$ without introducing the new variable $\mathcal{X}$, and $(c)$ plot evaluates the maximum tolerable error limit (security threshold) for sequence $S_{B2}$ with the introduction of the new variable $\mathcal{X}$.
• Figure 2: (Color online) Variation of secret key rate with bit-flip probability ($q$) and QBER ($\mathcal{E}$): $(a)$ lower bound on the secret-key rate of our protocol as a function of bit-flip probability and QBER, $(b)$ contour plot for lower bound error limit; QBER vs bit-flip probability, $(c)$ upper bound on the secret-key rate of our protocol as a function of bit-flip probability and QBER, and $(d)$ contour plot for upper bound error limit; QBER vs bit-flip probability.
• Figure 3: (Color online) Variation of Eve's information with distance to obtain critical distance ($l_{c}$): $(a)$ Eve's information as a function of distance to estimate the critical distance at which the attacker gains maximum key information by the PNS attack on Protocol 1, $(b)$ Eve's information as a function of distance to estimate the critical distance at which the attacker gains maximum key information by the IRUD attack on Protocol 2.