Benchmarking quantum key distribution by mixing single photons and laser light

TL;DR

The paper addresses enhancing BB84 QKD by incoherently mixing a quantum-dot single-photon source (QDS) with Poissonian laser light (PDS). It develops a phenomenological hybrid-statistics model and validates it experimentally, showing that mixing can boost the secret-key rate (SKR) at short distances while preserving long-distance performance with pure QDS; an explicit SKR bound under GLLP-like security is derived. The results reveal an advantage threshold for single-photon versus Poissonian statistics and demonstrate that the advantage shifts with QDS brightness and single-photon purity, providing practical guidelines for optimizing SKR via tunable mixing. Overall, the work introduces a flexible, tunable approach to boost QKD performance in realistic hardware by combining SPS and PDS, with clear implications for source design and deployment in quantum networks.

Abstract

Quantum key distribution is a key application of quantum mechanics, shaping the future of privacy and secure communications. Many protocols require single photons, often approximated by strongly attenuated laser pulses. Here, we harness the emission of a quantum dot embedded in a micropillar and explore a hybrid approach where the information is encoded on a mixture of single photons and laser pulses. We derive a phenomenological analysis of the configuration where both sources of light are mixed incoherently to perform the BB84 protocol, showing nearly perfect matching between theory and experiment. This provides a flexible technology compensating limited collected brightnesses of single-photon sources as well as a thorough investigation of single-photon statistics advantage scenarios over Poisson-distributed statistics. Explicitly, our model highlights an efficiency threshold for unconditional advantage of single photons over laser along with insights on the interplay between single-photon purity and collected brightness in the performances of BB84.

Figures (8)

• Figure 1: BB84 implementation with a QDS. Photons are produced by exciting the QD, operating in a 4 K cryostat, with blue-detuned laser light by $\Delta_{\text{LA}}$. The excitation laser is split into two different paths using a 50:50 fibered beam-splitter (FBS). One path is used to excite the QD, and the laser light is later suppressed with three bandpass filters with two (green) mounted on motorized stages. The second path contains a delay line to temporally match laser pulses and single photons that are recombined with a 99:1 fibered coupler. The photons are linearly polarized using a linear polarizer (red) and a quarter (green) and a half waveplate (yellow). A polarizing beam splitter (PBS) allows a small pick-off of the photons into a Hanbury Brown and Twiss (HBT) measurement setup. The four BB84 states are encoded using another pair of half and quarter waveplates. After the variable optical attenuator (VOA) used to emulate losses over long fiber links, a polarization analyser setup enables randomized measurements in two orthogonal bases: $\{|H\rangle, |V\rangle\}$ and $\{|D\rangle, |A\rangle\}$ with two waveplates and one Wollaston prism (WP) on each arm. The events measured on superconducting nanowire single-photon detectors (SNSPDs) are monitored and processed using a time tagging device.
• Figure 2: Distance scalings of the SKR for different mixed statistics. The secret key rate in bits per pulse is measured over attenuation for different mixed statistics, corresponding to different amounts of poissonian light sent among single photons to Bob (experiment : data points, simulation : lines). The ratio of the photons coming from the two types of statistics is given by the ratio of their mean photon numbers. The attenuation is mapped to distance assuming direct operation in the telecom C-band, using commercial fibers with linear attenuation $\alpha =$ 0.21 dB/km.
• Figure 3: SKR distance scalings and optimized parameters of the mixed statistics as a function of attenuation. a) The SKR is measured over several attenuations for multiple amounts of Poissonian light used by Alice. The maximum SKR obtained for each attenuation is plotted (purple dots) and compared to the theoretical model (purple solid line). As comparison, the SKR distance scaling using only single photons from our source is plotted in pink, and the measured SKR using only laser is plotted with the blue crosses, compared to the theoretical curve in blue solid line. b) Comparison of the experimental (symbols) optimal relative laser mean photon number (red) and single photon purity $\mathcal{P} = 1 - g^{(2)}(0)$ (purple) with our model (solid lines).
• Figure 4: Optimal mean photon number ratio for different collected brightnesses and corresponding distance scaling scenarios. a) Simulated optimal relative mean photon ratio of the laser leading to the best SKR at various distances. b) Comparison of the simulated SKR distance scaling obtained with single photons for different configurations. Ths SKR obtained with a QDS with $g^{(2)}(0) = 1\,\%$ with different collected brightnesses is plotted as a function of attenuation (solid lines), as well as the SKR obtained with a QDS in the case where $g^{(2)}(0) = 0.01\,\%$ with collected brightness of 50 %.
• Figure 5: Scanning parameters to compute the secret key rate (SKR). Two parameters are measured for 20 $\times$ 20 different sets of filter positions (20 positions each): a) the raw count rate at Bob's end and b) the second-order autocorrelation function at time delay zero $g^{(2)}(0)$. The grey areas indicate positions for which the computation of the $g^{(2)}(0)$ was not possible either due to the saturation of the SNSPDs or to a low count rate.