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arXiv:2409.07939 · PRX Quantum

Decoy-State and Purification Protocols for Superior Quantum Key Distribution with Imperfect Quantum-Dot-Based Single-Photon Sources: Theory and Experiment

Yuval Bloom, Yoad Ordan, Tamar Levin, Kfir Sulimany, Eric G. Bowes, Jennifer Ann Hollingsworth, Ronen Rapaport

Published Jul 14, 2025• 6 citations
arXivHTMLPDF

Abstract

The original proposal of quantum key distribution (QKD) was based on ideal single-photon sources, which, 40 years later, are still challenging to develop. Therefore, the development of decoy-state protocols using weak coherent states (WCS) from lasers set the frontier in terms of secure-key rates and distances. Here, we propose and experimentally demonstrate two simple-to-implement QKD protocols that allow practical far from ideal sub-Poissonian photon sources to outperform state-of-the-art WCS. By engineering the photon statistics of a biexciton-exciton cascade in room-temperature single-photon sources based on giant colloidal quantum dots coupled to nanoantennas, we show that either a truncated decoy-state protocol or a heralded-purification protocol can be employed to achieve a significantly increased performance in terms of the maximal allowed channel loss for secure-key creation, which can exceed even that of ideal WCS by more than 3 dB. We then experimentally emulate a BB84 QKD using such a quantum dot source, verifying the superiority of our protocols over the best possible BB84 WCS performance. These protocols can be utilized efficiently on a host of various quantum emitters having controllable photon statistics with a finite photon-number basis, offering a practical approach to QKD without the hindering requirements on the single-photon purity of the photon source.

DOI
10.1103/7fdd-m92n

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The original proposal of quantum key distribution (QKD) was based on ideal single-photon sources, which, 40 years later, are still challenging to develop. Therefore, the development of decoy-state protocols using weak coherent states (WCS) from lasers set the frontier in terms of secure-key rates and distances. Here, we propose and experimentally demonstrate two simple-to-implement QKD protocols that allow practical far from ideal sub-Poissonian photon sources to outperform state-of-the-art WCS. By engineering the photon statistics of a biexciton-exciton cascade in room-temperature single-photon sources based on giant colloidal quantum dots coupled to nanoantennas, we show that either a truncated decoy-state protocol or a heralded-purification protocol can be employed to achieve a significantly increased performance in terms of the maximal allowed channel loss for secure-key creation, which can exceed even that of ideal WCS by more than 3 dB. We then experimentally emulate a BB84 QKD using such a quantum dot source, verifying the superiority of our protocols over the best possible BB84 WCS performance. These protocols can be utilized efficiently on a host of various quantum emitters having controllable photon statistics with a finite photon-number basis, offering a practical approach to QKD without the hindering requirements on the single-photon purity of the photon source.
Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) enables secure communication without trusting the measurement devices, but its performance critically depends on the quality of the employed photon sources. We compare MDI-QKD implementations based on Weak Coherent Pulses (WCPs) with those employing Quantum Dot (QD) single-photon sources. WCP-based schemes are fundamentally limited by Poissonian photon-number statistics, imposing a trade-off between single- and multi-photon emissions, whereas QD sources exhibit sub-Poissonian statistics with low antibunching parameter g(2)(0)g^{(2)}(0)g(2)(0). Using a decoy-state analysis for both source types, we find that even at moderate mean photon numbers, QD-based implementations outperform the best-case WCP configuration - where the mean photon number is optimised at each transmission distance - across the full range of transmission distances. We further incorporate the effect of imperfect photon indistinguishability via Hong-Ou-Mandel interference visibilities into the security framework and demonstrate that both source types are highly sensitive to even small deviations from ideal indistinguishability, significantly affecting achievable key rates and maximum transmission distance.
Quantum key distribution (QKD) relies on single photon sources (SPSs), e.g. from solid-state systems, as flying qubits, where security strongly requires sub-Poissonian photon statistics with low second-order correlation values ($g^{(2)}(0)$). However, achieving such low $g^{(2)}(0)$ remains experimentally challenging. We therefore propose a decoy-like QKD protocol that relaxes this constraint while maintaining security. This enables the use of many SPSs with $g^{(2)}(0) > $0.1, routinely achieved in experiments but rarely considered viable for QKD. Monte Carlo simulations and our experiment from defects in hexagonal boron nitride show that, under linear loss, $g^{(2)}(0)$ remains constant, whereas photon-number-splitting (PNS) attacks introduce nonlinear effects that modify the measured $g^{(2)}(0)$ statistics. Exploiting this $g^{(2)}(0)$ variation as a diagnostic tool, our protocol detects PNS attacks analogously to decoy-state methods. Both single- and two-photon pulses consequently securely contribute to the secret key rate. Our protocol outperforms the Gottesman--Lo--Lutkenhaus--Preskill (GLLP) framework under high channel loss across various solid-state SPSs and is applicable to the satellite-based communication. Since $g^{(2)}(0)$ can be extracted from standard QKD experiments, no additional hardware is required. The relaxed $g^{(2)}(0)$ requirement simplifies the laser system for SPS generation. This establishes a practical route toward high-performance QKD without the need for ultra-pure SPSs.
Weak coherent source (WCS) and spontaneous parametric down converted heralded single photon pairs have found applications in quantum key distribution (QKD) and quantum imaging (QI) experiments. Decoy state methods have also been used to enhance the security for QKD and QI. We study quantum secured imaging with the decoy state heralded single photon source (HSPS). The HSPSs superior performance in low photon number regimes makes it an ideal candidate for integrating quantum key distribution protocols to reduce measurement uncertainty and ensure secure QI. Furthermore, our results also infer the influence of the decoy state WCS, due to its higher operating speed than decoy state HSPS, would be effective in conditions that allow higher mean photon numbers for quantum secured imaging.
Global quantum secure communication can be achieved using quantum key distribution (QKD) with orbiting satellites. Established techniques use attenuated lasers as weak coherent pulse (WCP) sources, with so-called decoy-state protocols, to generate the required single-photon-level pulses. While such approaches are elegant, they come at the expense of attainable final key due to inherent multi-photon emission, thereby constraining secure key generation over the high-loss, noisy channels expected for satellite transmissions. In this work we improve on this limitation by using true single-photon pulses generated from a semiconductor quantum dot (QD) embedded in a nanowire, possessing low multi-photon emission (<10−6<10^{-6}<10−6) and an extraction system efficiency of -15 dB (or 3.1%). Despite the limited efficiency, the key generated by the QD source is greater than that generated by a WCP source under identical repetition rate and link conditions representative of a satellite pass. We predict that with realistic improvements of the QD extraction efficiency to -4.0 dB (or 40%), the quantum-dot QKD protocol outperforms WCP-decoy-state QKD by almost an order of magnitude. Consequently, a QD source could allow generation of a secure key in conditions where a WCP source would simply fail, such as in the case of high channel losses. Our demonstration is the first specific use case that shows a clear benefit for QD-based single-photon sources in secure quantum communication, and has the potential to enhance the viability and efficiency of satellite-based QKD networks.
Quantum key distribution (QKD) allows for provably secure key distribution between two trusted parties. Because the security and performance of QKD protocols rely on devices that behave according to specific assumptions, idealized or inaccurate assumptions about device behavior can introduce security loopholes. Real devices can never be perfectly characterized, and their performance metrics are always subject to certain error margins, which must be accounted for in a rigorous theoretical analysis. Only recently have rigorous finite-size results allowed for imperfect characterizations of devices (where device parameter have uncertainty margins) - an advance yet to be considered in experimental implementations of the BB84 protocol. In this work, we prove the security and analyze the performance of an implementation of the BB84 protocol using single photons generated by a semiconductor quantum dot light source in combination with dynamic polarization-state encoding. We consider the presence of incompletely characterized devices by accounting for imperfections in the single-photon source (in terms of finite g(2)(0)) as well as the receiver (non-ideal beam-splitters, finite detector efficiencies, and dark counts), all with error margins. The resulting protocol implementation shows competitive performance, paving the way towards practical and loop-hole free implementations of QKD.
Reference-frame-independent quantum key distribution (RFI QKD) can generate secret keys without the alignment of reference frames, which is very robust in real-life implementations of QKD systems. However, the performance of decoy-state RFI QKD with both source errors and statistical fluctuations is still missing until now. In this paper, we investigate the performance of decoy-state RFI QKD in practical scenarios with two kinds of light sources, the heralded single photon source (HSPS) and the weak coherent source (WCS), and also give clear comparison results of decoy-state RFI QKD with WCS and HSPS. Simulation results show that the secret key rates of decoy-state RFI QKD with WCS are higher than those with HSPS in short distance range, but the secret key rates of RFI QKD with HSPS outperform those with WCS in long distance range.