A Fully Device-Independent Ternary Quantum Key Distribution Protocol Based on the Impossible Colouring Game

TL;DR

This work proposes a Ternary Fully Device-Independent Quantum Key Distribution protocol based on the two-party Impossible Colouring pseudo-telepathy game, utilizing maximally entangled qutrit states to enable secure key generation between distant parties.

Abstract

We propose a Ternary Fully Device-Independent Quantum Key Distribution (TFDIQKD) protocol based on the two-party Impossible Colouring pseudo-telepathy game, utilizing maximally entangled qutrit states to enable secure key generation between distant parties. The protocol harnesses Bell inequality violations that arise from contextuality in the Kochen-Specker theorem, thereby offering a quantum advantage in a task that is classically impossible and eliminating reliance on assumptions about the internal functioning of quantum devices. A specially designed qutrit quantum circuit is used for state preparation. Security and device independence are rigorously analyzed within a composable framework, employing Bell-inequality violations, smooth min-entropy, von Neumann entropy, and Shannon entropy. The protocol achieves optimal key rates in the ideal case and maintains security under significant noise, with a finite-key analysis that supports its practical viability. Overall, the protocol operates within an adequate security framework and demonstrates an improved key generation rate compared to standard quantum key distribution schemes, highlighting the potential of high-dimensional quantum systems for secure communication.

Figures (4)

• Figure 1: Generic DIQKD Protocol.
• Figure 2: The orthogonality graph of the Conway-Kochen Set of 31 vectors, denoted as $\mathcal{G}$. Note that an edge exists between two nodes if and only if the vectors corresponding to the nodes are orthogonal to each other. Extensive details about the vectors are provided in Table .
• Figure 3: Variation of mutual information $H(X:Y)$ with error rate $\eta$ for different values of the correlation parameter $c$. Mutual information decreases as the error rate increases, with the rate of decline dependent on $c$. Negative values of $c$ (dashed lines) show mutual information greater than $1$, which is contradictory, and are thus discarded, while positive values (solid lines) retain high mutual information at most $1$. The curves correspond to: dashed blue for $c = -2.0$, dashed orange for $c = -1.5$, dashed green for $c = -1.0$, dashed red for $c = -0.5$, solid violet for $c = 0.5$, solid brown for $c = 1.0$, solid magenta for $c = 1.5$, solid gray for $c=2.0$, and solid olive for $c=2.5$
• Figure 4: Key rate as a function of error rate $\eta$. The solid blue curve represents our derived key rate, which decreases monotonically with increasing error. The vertical red dashed line indicates the raw key rate upper bound, beyond which secure key generation is not feasible. The plot highlights the trade-off between noise and secure communication rate in the protocol.