Harnessing Hybrid Frequency-Entangled Qudits through Quantum Interference

TL;DR

This work tackles the challenge of scalable HD time–frequency quantum information by introducing hybrid frequency-entangled qudits (HFEQs), a DV-CV entangled state produced via Hong–Ou–Mandel interference in the frequency domain. The authors develop an integrated interferometer that jointly implements HOM and Franson interference to discretize the SPDC joint spectral amplitude into a DV frequency-bin structure while preserving intra-bin CV entanglement. Experimentally, they generate and manipulate HFEQs with dimensions $D=5,7,9,11$ over a 770 m campus fiber, achieving global Franson visibilities $>98\%$ and per-bin visibilities $\sim95$–$99\%$ after background subtraction; they also extract Schmidt-number bounds $K_F$ that exceed the maximum for conventional FEQs, indicating stronger overall entanglement. The results provide a robust DV-CV resource for HD time–frequency quantum information processing and offer new insights into HOM-based FEQs, with potential applications in QKD, grid-state quantum error correction, and hybrid DV–CV QIP.

Abstract

High-dimensional (HD) quantum entanglement expands the Hilbert space, offering a robust framework for quantum information processing with enhanced capacity and error resilience. In this work, we present a novel HD frequency-domain entangled state, the hybrid frequency-entangled qudit (HFEQ), generated via Hong-Ou-Mandel (HOM) interference, exhibiting both discrete-variable (DV) and continuous-variable (CV) characteristics in the frequency domain. By tuning HOM interference, we generate and control HFEQs with dimensions $D=5,7,9,11, confirming their DV nature. Franson interferometry confirms the global frequency correlations with visibility exceeding 98% and verifies the CV entanglement within individual frequency modes with visibility greater than 95%. Our findings provide deeper insight into the physical nature of frequency-entangled qudits generated by quantum interference and introduce a novel resource for HD time-frequency quantum information processing.

Figures (12)

• Figure 1: (a) Schematic diagram of the integrated quantum interferometer. PBS: Polarizing beam splitter; HWP: Half-wave plate; QWP: Quarter-wave plate; CC: Coincidence counting measurement. (b) Schematic diagram of the coincidence counting measurement for the conditional state. $\tau_{s'}$ and $\tau_{i'}$ denotes the detected timing of $s'$-mode and $i'$-mode photons, respectively.
• Figure 2: Demonstration of a series of highly anti-correlated TPES JSIs under constructive HOM interference. In (a)-(c), we examine a degenerate JSI with a series of HOM delay times $\tau_H$ of $0$, $12/\Delta\omega_S$, and $20/\Delta\omega_S$, respectively. (d)-(f) show the reduced signal mode spectrum of (a)-(c). The pump laser bandwidth is set to $\Delta\omega_p=\Delta\omega_S/20$ for all cases.
• Figure 3: Comparison of HOM visibility and frequency correlation of HFEQs. (a)-(c) The JSIs of HFEQs with $\tau_H=16/\Delta\omega_S$ under a series of pump bandwidths (as shown in labels). (d)-(f) The corresponding single-photon spectrum of (a)-(c), respectively. (g) The relationship between the Schmidt number of HFEQs, $K_F$, and pump bandwidth. (h) The relationship between $K_F$ and HOM visibility, $V_H$.
• Figure 4: Simulations of different bandwidth-pumped SPDC JSIs under HOM and Franson interference for various Franson delays $\tau_F$. In all cases, the HOM delay is set to $\tau_H=20/\Delta\omega_S$. Each row of figures corresponds to the same pump bandwidth: (a)-(c) $\Delta\omega_p=0.05\Delta\omega_S$, (d)-(f) $\Delta\omega_p=0.5\Delta\omega_S$, and (g)-(i) $\Delta\omega_p=\Delta\omega_S$. Each column of figures corresponds to the same Franson delay: (a)-(g) $\tau_F=2/\Delta\omega_S$, (b)-(h) $\tau_F=10/\Delta\omega_S$, and (c)-(i) $\tau_F=20/\Delta\omega_S$. The white dashed line represents the trough location of $\cos^2(\Omega_{+}\tau_F/2)$, and the white solid line denotes the distribution of origin SPDC JSI. (j) shows the TPI fringes of different bandwidth-pumped SPDCs under HOM and Franson interference. The gray area represents the signal-photon interference region which will be avoided in the Franson interferometer. The pump frequency is set at $\omega_p=20\Delta\omega_s$ to clearly demonstrate the Franson interference fringe. Notably, (f) and (i) present particular grid structures in the joint spectrum, which will be discussed in Appendix.\ref{['GKP_states']}.
• Figure 5: (a) Fiber network (yellow line) in NCU campus. (b) Schematic diagram of the experimental setup. DCF: Dispersion compensating fiber. ToFS: Time-of-flight spectrometer. C.C.: coincidence counting.