## 5 Improved Setup with a Fully Active Base Selection
### Proposed Defense Strategy against Strong-Light Attacks
In addition, the communication-induced coincidence probabilities would become smaller, and thus the ratio of the probability of blinding-induced coincidences would increase in comparison to  
Figure 5: Flow chart of the defense strategy for the proposed receiver in Figure 4.  
ones from the communication. This would make [PERSON]'s attack more easily discoverable. On the other hand, she could increase \(p_{QInTot}\) by removing a loss she induced beforehand or part of it, as explained previously, if any. In that case, she must \"invent\" new qubits for [PERSON] that would cause an increase in the BER, causing [PERSON] and [PERSON] to remove this extra information in the privacy amplification so that [PERSON] will not gain any new knowledge about the key and nor would the effective key length change. In this way, her discoverability would decrease by the factor with which she enlarged \(p_{QInTot}\), but this is not a significant gain, as will be shown below. Before moving to the final step, one needs to estimate the statistical uncertainty of \(\epsilon_{\text{Q}Clh}\). To that end, I assume that the predominant uncertainty of \(p_{QInTot}\) comes from the statistical uncertainties of \(f_{QInTot}\) and the dark count rates. I further assume that qubit detection and dark counts are Poissonian events, it is then straightforward to show, using the standard statistical theory of the propagation of uncertainty, that its variance is given by  
\[\sigma_{\text{Q}Clh}^{2}=\left(\frac{\sigma_{QInTot}^{2}}{f_{G}^{2}}+16t_{G}^ {2}\sigma_{\text{D}CR}^{2}\right)\left(\frac{(1-p_{QInTot})^{\frac{1}{(\phi)} -1}}{\langle n\rangle\epsilon_{B}}\right)^{2}. \tag{15}\]  
At the end of this step, the following parameters pertaining to the hardware and the quantum communication are known: \(\langle n\rangle\), \(f_{G}\), \(t_{G}\), \(\epsilon_{B}\), \(f_{DCR}\), \(\sigma_{\text{D}CR}\), \(p_{QIn}^{\prime}\), \(p_{QOut}^{\prime}\), \(\epsilon_{\text{Q}Clh}\), and \(\sigma_{\text{Q}Clh}\). These are input into the final step. **In the third and final step**, one calculates the upper limits on the probabilities of the in- and out-of-gate coincidence probabilities for an undisturbed QKD communication (\(p_{ClInTHR}\) and \(p_{CountHR}\)) and compares them to the directly measured probabilities of the in- and out-of-gate coincidences (\(p_{QIn}^{\prime}\) and \(p_{QOut}^{\prime}\)) in order to detect whether the QKD system is under attack at a desired (arbitrary) level of confidence. The in- and out-of-gate undisturbed coincidence probabilities \(p_{Cln}\) and \(p_{COut}\) can be estimated using Equations (5) and (8), respectively, and the parameters are available from the previous step. Their respective variances are  
\[\sigma_{Cln}^{2}=4t_{G}^{4}f_{DCR}^{4}+\frac{\langle n\rangle^{4}e_{g}^{4}e_{ QCh}^{4}}{16}\bigg{(}\frac{\sigma_{\text{Q}Clh}}{\epsilon_{\text{Q}Clh}} \bigg{)}^{2} \tag{16}\]  
\[\sigma_{\text{C}Out}^{2}=4\bigg{(}\frac{1}{f_{G}}-t_{G}\bigg{)}^{4}f_{DCR}^{4} \bigg{(}\frac{\sigma_{\text{D}CR}}{f_{DCR}}\bigg{)}^{2}\,. \tag{17}\]  
Next, without any assumption about the statistical distribution(s) governing their values, one can find the respective upper limits on these probabilities, using Chebyshev's inequality [32]  
\[p(p_{Cln}\geq p_{ClnTHR})\leq\frac{\sigma_{Cln}^{2}}{p_{ClnTHR}^{2}}. \tag{18}\]  
Keeping in mind that all variables in the above equation are positive, an upper limit on \(e_{QCh}^{\prime}\) is given by  
\[p_{ClnTHR}\leq\frac{\sigma_{Cln}}{\sqrt{p(p_{Cln}\geq p_{ClnTHR})}} \tag{19}\]  
which can be interpreted as  
\[p_{QInTot}=1-\left(1-\epsilon_{B}\epsilon_{QCh}\right)^{\langle n\rangle}. \tag{13}\]0  
where \(p_{CONF}\) is an arbitrarily chosen probability (confidence level) that inequality \(p_{Cln}<p_{ClnTHR}\) holds. Equivalently, I obtain  
\[p_{QInTot}=1-\left(1-\epsilon_{B}\epsilon_{QCh}\right)^{\langle n\rangle}. \tag{13}\]1Finally, I define the following security criterion. If the inequalities  
\[ \begin{array}{l}p^{\prime}_{CIn}<p_{CInTHR}\\ p^{\prime}_{COut}<p_{COutTHR}\end{array}