Chip-to-Chip Hyperentanglement Distribution

• Chip-to-chip hyperentanglement distribution is the process by which quantum information encoded in multiple degrees-of-freedom is generated, transmitted, and manipulated using integrated photonic chips.
• It employs techniques such as spontaneous four-wave mixing, interferometric demultiplexing, and phase-locked loop stabilization to maintain high entanglement fidelity over optical fibers.
• Its integrated purification protocols using deterministic CNOT operations pave the way for scalable quantum repeater architectures and robust quantum communication.

Chip-to-chip hyperentanglement distribution denotes the process by which quantum information encoded in multiple, independent degrees of freedom (DoF)—such as path, polarization, time-bin, frequency-bin, and spatial mode—is generated on a photonic chip, coherently transmitted via optical links (typically fiber), and subsequently decoded and manipulated on a separate, remote chip. Hyperentanglement distribution is a foundational technology for scalable photonic quantum networks, quantum repeaters, and modular quantum processors, as it enables high information capacity, parallelism, and robustness against noise and decoherence.

1. Generation of Path-Encoded High-Dimensional Entanglement

The on-chip generation of high-dimensional, path-encoded entangled photon pairs is realized via spontaneous four-wave mixing (SFWM) in multi-path silicon waveguides. For example, four parallel “snake-shaped” silicon waveguides on the source chip (designated “Charlie”) are simultaneously pumped by a continuous-wave laser. SFWM in each waveguide produces a photon pair—signal and idler—which, after asymmetric Mach–Zehnder interferometer (AMZI) demultiplexing and balancing of amplitudes and phases, yields a four-dimensional (ququart) maximally entangled state:

$$|\phi\rangle = \frac{1}{2} (|00\rangle + |11\rangle + |22\rangle + |33\rangle)$$

where the indices 0–3 denote distinct on-chip path modes.

These path-encoded states are readily scalable to higher dimensions by increasing the number of waveguide channels. Integrated photonics enables precise tuning of phase (via on-chip heaters, Vπ ≈ 2.5 V) and amplitudes, while low-loss design (waveguide losses ~5 dB/cm) preserves the quantum state’s fidelity.

2. Conversion to Fiber-Based Polarization–Spatial Hyperentanglement

To facilitate robust transmission over optical fibers, the chip leverages two-dimensional grating couplers (2D GCs) that coherently map each on-chip path mode to a specific combination of fiber spatial and polarization modes:

• |0⟩ → |0H⟩
• |1⟩ → |0V⟩
• |2⟩ → |1H⟩
• |3⟩ → |1V⟩

Applying this mapping to both signal and idler photons transforms the initial four-dimensional path-entangled state into a product hyperentangled state in fiber:

$$|\phi\rangle = |\phi^+\rangle_\mathrm{spatial} \otimes |\Phi^+\rangle_\mathrm{polarization} = \frac{1}{2} (|00\rangle + |11\rangle) \otimes (|HH\rangle + |VV\rangle)$$

This process generates a Bell state in each DoF, realizing genuine hyperentanglement suitable for transmission over standard telecom fibers.

An on-chip optical phase-locked loop (PLL)—comprising a phase monitor, PID controller, and external phase shifter—actively stabilizes the relative phase between fibers, which is vital for maintaining spatial-mode coherence during chip-to-chip distribution.

3. Chip-to-Chip Transmission and Phase Stabilization

The hyperentangled photon pairs, now encoded jointly in spatial and polarization DoFs, are launched into single-mode fibers and routed to a receiver silicon chip (“Bob”). To ensure interference visibility and quantum state fidelity across the fiber link, the optical PLL compensates for dynamic phase fluctuations between the two spatial-mode fibers. The PLL achieves phase stability within ±4.6%.

Upon arrival at the receiver, the quantum state can be further manipulated and analyzed via programmable on-chip interferometer networks, maintaining the mapping fidelity needed for subsequent quantum operations and entanglement purification.

4. On-Chip Entanglement Purification Protocols

A central advance in chip-to-chip hyperentanglement distribution is the realization of integrated entanglement purification using the spatial DoF as a “ancilla” consumed resource:

• The on-chip purification circuit, constructed from programmable waveguide crossings and Mach–Zehnder interferometers, implements a deterministic CNOT operation with the spatial mode as control and polarization as the target.
• After the CNOT transformation, paths with correlated errors are filtered by select waveguide ports (post-selection). This operation discards instances of bit-flip (BF) or phase-flip (PF) errors, thereby increasing the polarization qubit’s fidelity:

$F' = \frac{F_1 F_2}{F_1 F_2 + (1-F_1)(1-F_2)}$

where $F_1$ and $F_2$ are pre-purification fidelities of the polarization and spatial qubits, respectively.

Demonstrated on-chip, the protocol increased polarization fidelity from 0.738 to 0.848 after a 20% simulated BF error rate and boosted the CHSH S-parameter from below to above the classical threshold (e.g., S ≈ 2.2 after purification).

5. Impact on Quantum Repeater Architectures

The integrated chip-to-chip hyperentanglement distribution with on-chip purification is a critical step toward photonic quantum repeaters. A complete quantum repeater requires on-chip realization of three pillars:

1. Entanglement swapping—already demonstrated on chip.
2. Quantum memory—progressing in nanophotonic platforms.
3. Entanglement purification—now implemented entirely on silicon photonics.

By addressing the scalability, stability, and controllability limitations that plagued earlier discrete-optics purification schemes, this approach enables modular, monolithically-integrated quantum repeater nodes. The architecture is inherently compatible with CMOS fabrication, supporting mass deployment.

6. Experimental Challenges and Optimization

While integrated photonic solutions offer robust performance, practical challenges remain:

• Coupling losses at 2D GCs are typically 5–6 dB, impacting link efficiency.
• Further reduction of phase fluctuations beyond ±4.6% can benefit fidelity.
• Environmental noise and imperfect balancing of amplitudes/phases can be further mitigated by integrating inverse-designed couplers or real-time feedback.

Advanced error sources, such as residual PF errors, are addressed via pre-purification Hadamard operations on chip.

7. Technological Implications and Future Directions

The confluence of high-dimensional entanglement generation, coherent DoF conversion, PLL-based phase stabilization, and fully on-chip purification establishes a clear pathway to hyperentanglement-based quantum networks. These results demonstrate that silicon integrated photonics can:

• Support hyperentanglement distribution in multiple DoFs,
• Enable practical, scalable, and stable chip-to-chip quantum interconnects,
• Realize on-chip entire quantum repeater protocols necessary for overcoming channel losses in long-distance quantum communication.

Continued optimization of coupling, stability, and integration with quantum memories will further consolidate the foundation for global quantum networks constructed from chip-based repeaters.