Secure One-Sided Device-Independent Quantum Key Distribution Under Collective Attacks with Enhanced Robustness

TL;DR

The paper introduces a CJWR steering inequality–based 1sDI-QKD protocol that certifies security with trust in only Bob’s measurement device. It derives a closed-form asymptotic key-rate bound under collective attacks, $r^{1s m{DI}} \ge I(A_3:B_3) - \chi(B_3:E)$, which simplifies to $r^{1s m{DI}} \ge 1 - h(Q) - h\left( \frac{1 + \sqrt{(\mathcal{F}_3^2 - 1)/2}}{2} \right)$, tying Eve’s information directly to the observed CJWR violation $\mathcal{F}_3$ and QBER $Q$; under depolarizing noise this yields $F_3 = \sqrt{3}\,(1-2Q)$ and a critical $Q_c^{1sDI}=8.62\%$, demonstrating robustness beyond standard DI-QKD. The work also analyzes detection-efficiency thresholds and post-selection strategies, showing secure key rates down to $\eta_A \approx 74.5\%$ (post-selection) and outlining practical implications for near-term experiments. Overall, the approach offers a tractable, steering-based alternative to DI-QKD with concrete, analytic security guarantees and realistic performance benchmarks.

Abstract

We study the security of a quantum key distribution (QKD) protocol under the one-sided device-independent (1sDI) setting, which assumes trust in only one party's measurement device. This approach effectively provides a balance between the experimental viability of device-dependent (DD-QKD) and the minimal trust assumptions of device-independent (DI-QKD). An analytical lower bound on the asymptotic key rate is derived to provide security against collective attacks, in which the eavesdropper's information is limited only by the function of observed violation of a linear quantum steering inequality, specifically the three-setting Cavalcanti-Jones-Wiseman-Reid (CJWR) inequality. We provide a closed-form key rate formula by reducing the security analysis to mixtures of Bell-diagonal states by utilizing symmetries of the steering functional. We show that the protocol tolerates higher quantum bit error rates (QBER) than present DI-QKD protocols by benchmarking its performance under depolarizing noise. Furthermore, we explore the impact of detection inefficiencies and show that, in contrast to DI-QKD, which requires near-perfect detection, secure key generation can be achieved even with lower detection efficiency on the untrusted side. These findings highlight the advantages of 1sDI-QKD as a steering-based alternative for secure quantum communication and provide insights relevant for near-future experimental implementations.

Figures (4)

• Figure 1: Schematic of a one-sided device-independent QKD protocol. A source distributes entangled two-qubit states to Alice and Bob. Alice’s device is untrusted (black box), while Bob’s is fully trusted. Inputs $x, y \in \{1,2,3\}$ are chosen using trusted random number generators, yielding binary outcomes $a, b \in \{+1,-1\}$. Security is certified via quantum steering, e.g., violation of the CJWR inequality.
• Figure 2: Comparison of key rates (r) as a function of the QBER (Q). The red dashed line represents the key rate $r^{\mathrm{DI}}$ in the DI scenario based on Bell inequality violation. The blue solid line corresponds to the 1sDI key rate $r^{\mathrm{1sDI}}$ certified via CJWR steering inequality violation. The green dotted line shows the DD key rate $r^{\mathrm{DD}}$, where both parties' devices are trusted.
• Figure 3: Comparison of secret key rates $r$ as a function of Alice’s detection efficiency $\eta_A$ under ideal visibility ($\nu = 1$) for a 1sDI-QKD protocol. The red dashed curve corresponds to the key rate without post-selecting QBER (Eq. \ref{['WithoutPostselected']}), while the blue solid curve represents the post-selected case (Eq. \ref{['WithPostselected']}), where QBER is constant. Post-selection allows secure key generation at lower detection efficiencies, down to $74.5\%$, highlighting a practical advantage over fully device-independent QKD.
• Figure 4: Threshold detection efficiency of Alice's device $\eta_A$ (in %) required for a positive secret key rate $r^{1sDI}> 0$ as a function of the source visibility $\nu$. The non-postselected strategy is denoted by the red dashed line, while the postselection case is represented by the solid blue line.

Theorems & Definitions (4)

• Lemma 1: Reduction to a two-qubit subspace
• proof
• Lemma 2: Reduction to Bell-diagonal form
• proof