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.
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.
Advancements in practical single-photon sources (SPS) exhibiting high brightness and low g(2)(0) have garnered significant interest for their application in quantum key distribution (QKD). To assess their QKD performance, it is essential to compare them with the widely employed weak coherent pulses (WCPs) in the decoy state method. In this work, we analyze the non-decoy efficient BB84 protocol for an SPS, partially characterising its photon statistics by its g(2)(0) and mean photon number. We compare it to the 2-decoy efficient BB84 with WCPs within the finite-key analysis framework while optimizing the parameters of both protocols. Our findings indicate that the non-decoy SPS with a mean photon number of ⟨n⟩=0.5 and g(2)(0)=3.6% can enhance the secure key generation over the 2-decoy WCP for block sizes under 4.66⋅109 sent signals (29 seconds of acquisition time) at a channel loss of 10 dB (52.5 km of optical fibre). Additionally, we demonstrate an increase in the maximum tolerable channel loss for SPSs with mean photon number ⟨n⟩≥0.0142 at block sizes below 108 sent signals (0.62 seconds of acquisition time). These results suggest that SPSs hold potential for key rate enhancement in short-range QKD networks, though further research is required to evaluate their key generation capabilities when integrated into the decoy method.
Quantum Key Distribution (QKD) enables the sharing of cryptographic keys secured by quantum mechanics. The BB84 protocol assumes single-photon sources, but practical systems rely on weak coherent pulses vulnerable to Photon-Number-Splitting (PNS) attacks. The Gottesman-Lo-Lütkenhaus-Preskill (GLLP) framework addresses these imperfections, deriving secure key rate bounds under limited PNS scenarios. The decoy-state protocol further improves performance by refining single-photon yield estimates, but still considers multi-photon states as insecure, thereby limiting intensities and constraining key rate and distance. More recently, finite-key security bounds for decoy-state QKD have been extended to address general attacks, ensuring security against adversaries capable of exploiting arbitrary strategies. In this work, we focus on a specific class of attacks, the generalized PNS attack, and demonstrate that higher pulse intensities can be securely used by employing Bayesian inference to estimate key parameters directly from observed data. By raising the pulse intensity to 10 photons, we achieve a 50-fold increase in key rate and a 62.2% increase in operational range (about 200 km) compared to the decoy-state protocol. Furthermore, we accurately model after-pulsing using a Hidden Markov Model (HMM) and reveal inaccuracies in decoy-state calculations that may produce erroneous key-rate estimates. While this methodology does not address all possible attacks, it provides a new approach to security proofs in QKD by shifting from worst-case assumption analysis to observation-dependent inference, advancing the reach and efficiency of discrete-variable QKD protocols.
We propose a simple quantum-key-distribution (QKD) scheme for practical single-photon sources (SPSs), which works even with a moderate suppression of the second-order correlation g (2) of the source. The scheme utilizes a passive preparation of a decoy state by monitoring a fraction of the signal via an additional beam splitter and a detector at the sender's side to monitor photon-number splitting attacks. We show that the achievable distance increases with the precision with which the sub-Poissonian tendency is confirmed in higher photon-number distribution of the source, rather than with actual suppression of the multiphoton emission events. We present an example of the secure key generation rate in the case of a poor SPS with g (2) =0.19, in which no secure key is produced with the conventional QKD scheme, and show that learning the photon-number distribution up to several numbers is sufficient for achieving almost the same distance as that of an ideal SPS.
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.
The existing decoy-state quantum key distribution (QKD) beating photon-number-splitting (PNS) attack provides a more accurate method to estimate the secure key rate, while it still considers that only single-photon pulses can generate secure keys in any case. However, multiphoton pulses can also generate secure keys if we can detect the possibility of PNS attack in the channel. The ultimate goal of this line of research is to confirm the absence of all types of PNS attacks. In particular, the PNS attack mentioned and detected in this paper is only the weaker version of PNS attack which significantly changes the observed values of the legitimate users. In this paper, under the null hypothesis of no weaker version of PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state protocols, extract a Cauchy distribution statistic, and further provide a detection method and the type I error probability. If the result is judged to be an attack, we can use the existing decoy-state method and the GLLP formula to estimate the secure key rate. Otherwise, the pulses with the same basis received including both single-photon pulses and multiphoton pulses, can be used to generate the keys and we give the secure key rate in this case. Finally, the associated experiments we performed (i.e., the significance level is 5%) show the correctness of our method.
Decoy-state methods are essential to perform quantum key distribution (QKD) at large distances in the absence of single-photon sources. However, the standard techniques apply only if laser pulses are used that are independent and identically distributed. Moreover, they require that the laser pulses are fully phase randomized. However, realistic high-speed QKD setups do not meet these stringent requirements. In this work, we generalize decoy-state analysis to accommodate laser sources that emit imperfectly phase-randomized states. We also develop theoretical tools to prove the security of protocols with lasers that emit pulses that are independent, but not identically distributed. These tools can be used with recent work [G. Curr\'as-Lorenzo, S. Nahar, N. L\"utkenhaus, K. Tamaki, and M. Curty, Quantum Sci. Technol. (2023)] to prove the security of laser sources with correlated phase distributions as well. We quantitatively demonstrate the effect of imperfect phase randomization on key rates by computing the key rates for a simple implementation of the three-state protocol.