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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

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.

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

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.

Paper Structure

This paper contains 9 sections, 45 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theory
  3. Equivalence between SWAP test and Hong-Ou-Mandel test
  4. HOM test for phase-randomized weak coherent pulses
  5. Experiment
  6. Results
  7. Discussion
  8. Conclusion
  9. Indistinguishability expressed by the trace of the density operator product

Figures (3)

  • Figure 1: Schematic of SWAP test. (a) Quantum circuit represented by quantum gates. (b) Photonic implementation. A controlled SWAP operation is constructed by a Mach-Zehnder interferometer (MZI) and Kerr nonlinearity. A single photon state $\ket{s}$ is the input for the upper MZI.
  • Figure 2: Experimental setup for HOM test. The top, middle, and bottom represent the state preparation part, the pulse thinning part, and the coincidence measurement part, respectively. LD: Laser Diode, AMZI: Asymmetric Mach-Zehnder Interferometer, OA: Optical Amplifier, ATT: Attenuator, PC: Polarization Controller, ABC: Automatic Bias Controller, PPG: Pulse Pattern Generator, BPF: Band Pass Filter, OSC: Oscilloscope, FM: Faraday Mirror, SNSPD: Superconducting Nanowire Single Photon Detector, TIA: Time Interval Analyzer.
  • Figure 3: Results of Hong-Ou-Mandel interference between adjacent pulses: (a) unmodulated pulses for reference, (b) pulses in X1-state and X0-state, (c) Y0-state and X0-state, and (d) Y1-state and X0-state. Coincidence counts were normalized using the value obtained at -26 ps. Red solid lines represent fitting results with a single set of parameters, while dotted lines represent fitting results using optimized parameters for each measurement group.