Autonomous Recognition of Erroneous Raw Key Bit Bias in Quantum Key Distribution

TL;DR

An abstract definition of a type of error that can occur with regard to the ratio of bit values in the raw key is presented, and how this has an impact on the security and key rate of QKD protocols.

Abstract

As Quantum Key Distribution technologies mature, it is pertinent to consider these systems in contexts beyond lab settings, and how these systems may have to operate autonomously. To begin, an abstract definition of a type of error that can occur with regard to the ratio of bit values in the raw key is presented, and how this has an impact on the security and key rate of QKD protocols. A mechanism by which errors of this type can be autonomously recognised is given, along with simulated results. A two part countermeasure that can be put in place to mitigate against errors of this type is also given. Finally some motivating examples where this type of error could appear in practice are presented to add context, and to illustrate the importance of this work to the development of Quantum Key Distribution technologies.

Figures (3)

• Figure 1: Logarithmic-scale plot of the number of bits from the Chernoff-Hoeffding bound against $\delta_\mu$ for different values of $\varepsilon$.
• Figure 2: a.) the probability distribution used to create the random key. The distribution mean changes from $1/2$ to $1/3$ once the SD error has occurred. b.) A simulation of Bob's estimated mean over time. The blue dashed line represents the nominal mean value, and the red dashed lines represent the upper and lower recognition thresholds. The first and second vertical orange dashed lines show where the SD error occurred, and where the recognition of the SD error was made respectively. This simulation was done with parameters $\delta_\mu=0.05$ and $\varepsilon=0.001$, hence a value for $t$ of $t=0.05$ was chosen as can be seen by the recognition thresholds.
• Figure 3: a.) This plot shows how the number of insecure raw key bits scales with the size of the sliding window. The dashed line shows the linear regression model that was fit to the dataset obtained via simulation. This coincides with the previously presented analytical result that showed that the proportion of insecure raw key bits scales linearly with the window size with a scaling factor of 0.3. b.) This plot shows the standard deviation of the results from the simulation. It was observed that this data exhibits a square-root scaling, and so a square-root regression model was fit to this data. The dashed line shows this regression model. For these simulations, the same parameters as with Fig. \ref{['fig:det_reg_attack']} were used, and 2500 simulations were run for each window size.