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arXiv:2603.26488

Hong-Ou-Mandel test to verify indistinguishability of the states emitted from a quantum key distribution transmitter implementing decoy Bennett-Brassard 1984 protocol

Toshiya Tajima, Akihisa Tomita, Atsushi Okamoto

quant-phSubmitted Mar 27, 2026• Announced Mar 30, 2026• 0 citations

v1 · Mar 27, 2026 v2 · May 26, 2026

Abstract

Quantum Key Distribution (QKD) systems require rigorous verification of device properties to ensure implementation security. A critical requirement is the indistinguishability of transmitted pulses encoded by different modulation patterns, as distinguishability through non-encoded degrees of freedom could enable undetected eavesdropping. We present a practical method for testing pulse indistinguishability in QKD transmitters based on Hong-Ou-Mandel (HOM) interference. We establish the theoretical equivalence between the SWAP test and HOM measurement for characterizing quantum state fidelity, demonstrating that HOM visibility directly relates to the trace of density matrix products for phase-randomized weak coherent pulses. We experimentally validated this approach using a high-speed QKD transmitter implementing the decoy BB84 protocol with time-bin encoding at 1.25 GHz. HOM interference was measured between adjacent pulses prepared in different Bennett-Brassard 1984 states (X0, X1, Y0, Y1) using superconducting nanowire single-photon detectors. The observed HOM visibility was approximately 0.3 across all state combinations, with no statistically significant differences detected. These results confirm that modulation does not compromise pulse indistinguishability in our transmitter. The HOM test provides a practical, quantum-optical method for security certification of QKD systems without requiring assumptions about specific degrees of freedom, using only standard fiber-optic components and single-photon detectors.

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Quantum Key Distribution (QKD) systems require rigorous verification of device properties to ensure implementation security. A critical requirement is the indistinguishability of transmitted pulses encoded by different modulation patterns, as distinguishability through non-encoded degrees of freedom could enable undetected eavesdropping. We present a practical method for testing pulse indistinguishability in QKD transmitters based on Hong-Ou-Mandel (HOM) interference. We establish the theoretical equivalence between the SWAP test and HOM measurement for characterizing quantum state fidelity, demonstrating that HOM visibility directly relates to the trace of density matrix products for phase-randomized weak coherent pulses. We experimentally validated this approach using a high-speed QKD transmitter implementing the decoy BB84 protocol with time-bin encoding at 1.25 GHz. HOM interference was measured between adjacent pulses prepared in different Bennett-Brassard 1984 states (X0, X1, Y0, Y1) using superconducting nanowire single-photon detectors. The observed HOM visibility was approximately 0.3 across all state combinations, with no statistically significant differences detected. These results confirm that modulation does not compromise pulse indistinguishability in our transmitter. The HOM test provides a practical, quantum-optical method for security certification of QKD systems without requiring assumptions about specific degrees of freedom, using only standard fiber-optic components and single-photon detectors.

Entanglement swapping enables the distribution of quantum states over long distances. In this protocol, a Bell state measurement projects photons, which were created in separate entangled photon sources, into an entangled state when their corresponding pairs interfere at a beamsplitter. This process is optimally realized when the photons are indistinguishable in all degrees of freedom, resulting in Hong-Ou-Mandel (HOM) interference. Since its initial proposal by [1], several experimental realizations have used pulsed, synchronized pumps, as in [2] to achieve temporal indistiguishability. In the case of continuous wave (CW) pumping, the sources are not synchronized, requiring post-selection of the coincidence events after detection. This requires detectors with a temporal resolution greater than the coherence time of the photons. Previous experiments have successfully observed HOM interference using periodically poled Lithium Niobate (ppLN) waveguides and superconducting nanowire single-photon detectors (SNSPDs) [3], also with hybrid sources to improve coincidence rates and HOM visibility [4], [5].

Due to the simplicity of Hong-Ou-Mandel (HOM) interferometer setup, it becomes very important in various quantum-based applications, especially when the photon indistinguishability is required such as measurement device independent quantum key distribution (MDI-QKD). In the present work, the HOM experiment setup is designed to study the quantum interference between two indistinguishable photons (frequency, time of arrival and polarization should be same for both photons) coming from two independent laser sources (attenuated laser). The aim is to achieve high visibility as it indicates the photon indistinguishability from two independent sources. Theoretically, the visibility is

50 \%

for indistinguishable photons from attenuated laser sources but in the experiment, due to various devices imperfections and other factors it is less than 50%. The HOM visibility achieved from our setup is

40 \%

tested for a distance of 20 km over standard single mode fiber (SMF). The main point to be noticed in this work is that, this experiment is performed using single photon avalanche diode.

Recently, the Hong–Ou–Mandel (HOM) interference between two independent weak coherent pulses (WCPs) has been paid much attention due to the measurement-device-independent (MDI) quantum key distribution (QKD). Using classical wave theory, articles reported before show that the visibility of this kind of HOM-type interference is ≤ 50%. In this work, we analyze this kind of interference using quantum optics, which reveals more details compared to the wave theory. Analyses confirm the maximum visibility of 50%. And we conclude that the maximum visibility of 50% comes from the two single-photon states in WCPs, without considering the noise. In the experiment, we successfully approach the visibility of 50% by using WCPs splitting from the single pico-second laser source and phase scanning. Since this kind of HOM interference is immune to slow phase fluctuations, both the realized and proposed experiment designs can provide stable ways of high-resolution optical distance detection.

Passive side-channel attacks in quantum key distribution (QKD) aim at obtaining information about the quantum signals without disturbing them and hence compromise real-world QKD security. Currently, there are no reliable tools for the assessment of QKD signal generation imperfections. In this work we propose a generic experimental method which allows to upper-bound QKD light-source imperfections and directly integrate them into the modern security proofs. The method relies on Hong-Ou-Mandel interference between different emitted signals: the maximum interference visibility reveals overall signal distinguishability that could lead to passive side-channel information leakage. We apply it for the standard decoy-state BB84 protocol and calculate a lower bound on the secret key rate for realistic values of interference visibility. The method can be readily implemented in practical QKD setups and is especially relevant for multiple-laser QKD systems such as the one installed on the Micius satellite.

Side-channel attacks on practical quantum key distribution systems compromise its security. Although some of these attacks can be taken into account, the general recipe of how to eliminate all side-channel flaws is still missing. In this work, we propose a method for estimation of the total passive side-channel information leakage from the Alice's light source. The method relies on Hong-Ou-Mandel interference between different signals emitted by Alice, which reveals their overall mode mismatch without the necessity to measure all individual degrees of freedom independently. We include experimental values of interference visibility in the security proof for the decoy-state BB84 protocol, and lower-bound the secure key rate for realistic light sources. The obtained results provide a tool that can be used for certification of the current QKD systems and pave the way towards the loophole-free design of the future ones.

The decoy-state method could effectively enhance the performance of quantum key distribution (QKD) with a practical phase randomized weak coherent source. Although active modulation of the source intensity is effective and has been implemented in many experiments, passive preparation of decoy states is also an important addition to the family of decoy-state QKD protocols. In this paper, following the theory of Curty et al. [Phys. Rev. A 81, 022310 (2010)], we experimentally demonstrate the phase-encoding passive-decoy-state QKD with only linear optical setups and threshold single-photon detectors. In our experiment, two homemade independent pulsed lasers, with visibility of Hong-Ou-Mandel interference $0.53(\ifmmode\pm\else\textpm\fi{}0.003)$, have been implemented and used to passively generate the different decoy states. Finally, a secret key rate of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$/pulse is obtained with 10-km commercial fiber between Alice and Bob.