Quantum key distribution protocol based on contextuality monogamy

The security of quantum key distribution (QKD) protocols hinges upon features of physical systems that are uniquely quantum in nature. We explore the role of quantumness, as qualified by quantum contextuality, in a QKD scheme. A QKD protocol based on the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) contextuality scenario using a three-level quantum system is presented. We explicitly show the unconditional security of the protocol by a generalized contextuality monogamy relationship based on the no-disturbance principle. This protocol provides a new framework for QKD which has conceptual and practical advantages over other protocols.

Figure 1

The KCBS orthogonality graph. Each vertex corresponds to a projector and the edge linking two projectors indicates their orthogonality relationship.

Figure 2

Alice and Bob are trying to violate the KCBS inequality [$K(A,B)]$, while Eve in her attempts to gain information is trying to violate the same inequality with Alice [$K(A,E)]$.

Figure 3

Joint commutation graph (top) of Alice-Bob KCBS test (thin-red line) and Alice-Eve KCBS test (thick-blue line) and its decomposition into two chordal subgraphs (below). Dotted edges indicate commutation relation between two projectors belonging to the two different KCBS tests.