Figure 1

Monogamy relations for different theories are plotted. The sufficient condition for the security of the key distribution protocol (24) is described by the line that passes through $P=[\frac{1}{2}(1+\frac{1}{\sqrt{2}}),\frac{1}{2}(1+\frac{1}{2\sqrt{2}})]$. The intersection of this line with monogamy relation for any specific theory $T$ gives the critical value of ${\beta }_T(\mathcal{A},\mathcal{B})$ above which Alice and Bob can have secure communication. More explicitly, if $\mathcal{A}$ and $\mathcal{B}$ estimate their $\beta (\mathcal{A},\mathcal{B})$ to be greater than ${\beta }_T(\mathcal{A},\mathcal{B})$, they can have secure communication against individual attacks of the eavesdropper who has access to the resources of theory $T$. Point $P$ has its horizontal coordinate equal to the Tsirelson bound, so for any theory $T$ that intersects the sufficient condition line before $P$, it is possible for $\mathcal{A}$ and $\mathcal{B}$ to have a quantum protocol secure against attacks from the $T$ regime. Note that the intersection of 1.1 monogamy with sufficient condition line is slightly before $P$. Therefore, quantum mechanics allows QKD secure against attacks by eavesdroppers from all three theories.Reuse & Permissions