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Chip-to-chip quantum teleportation and multi-photon entanglement in silicon
Daniel Llewellyn, Yunhong Ding, Imad I. Faruque, Stefano Paesani, Davide Bacco, Raffaele Santagati, Yan-Jun Qian, Yan Li, Yun-Feng Xiao, Marcus Huber, Mehul Malik, Gary F. Sinclair, Xiaoqi Zhou, Karsten Rottwitt, Jeremy L. O Brien, John G. Rarity, Qihuang Gong, Leif K. Oxenlowe, Jianwei Wang, Mark G. Thompson
TL;DR
The paper addresses the difficulty of producing multiple bright, pure, identical photons while integrating photon sources with high-fidelity multiqubit operations. It combines silicon microring-resonator sources with programmable linear-optic circuits to demonstrate teleportation and multipartite entanglement, including chip-to-chip single-qubit teleportation with reported fidelities of 0.940 ± 0.041 and 0.832 ± 0.048.
Problem
Scalable photonic quantum processing requires multiple high-quality single-photons, high-fidelity multiqubit operations, and seamless integration of nonlinear sources with linear circuits.
Method
The paper monolithically integrates programmable silicon microring-resonator sources with linear-optic circuits implementing Bell projection, fusion, and projective measurements.
Results
0.940 ± 0.041 and 0.832 ± 0.048 are the reported fidelities for chip-to-chip teleportation of single-qubit states.
Takeaways & Limitations
The experiments demonstrate a proof-of-principle silicon quantum transceiver capability for chip-to-chip teleportation and distributed quantum processing.
Takeaways & Limitations
Brightness estimation requires modification when multipair emission and nonlinear losses are significant, especially with non-photon-number-resolving detectors.
Abstract
from arXiv · showhide
Exploiting semiconductor fabrication techniques, natural carriers of quantum information such as atoms, electrons, and photons can be embedded in scalable integrated devices. Integrated optics provides a versatile platform for large-scale quantum information processing and transceiving with photons. Scaling up the integrated devices for quantum applications requires highperformance single-photon generation and photonic qubit-qubit entangling operations. However, previous demonstrations report major challenges in producing multiple bright, pure and identical single-photons, and entangling multiple photonic qubits with high fidelity. Another notable challenge is to noiselessly interface multiphoton sources and multiqubit operators in a single device. Here we demonstrate on-chip genuine multipartite entanglement and quantum teleportation in silicon, by coherently controlling an integrated network of microresonator nonlinear single-photon sources and linear-optic multiqubit entangling circuits. The microresonators are engineered to locally enhance the nonlinearity, producing multiple frequencyuncorrelated and indistinguishable single-photons, without requiring any spectral filtering. The multiqubit states are processed in a programmable linear circuit facilitating Bell-projection and fusion operation in a measurement-based manner. We benchmark key functionalities, such as intra-/inter-chip teleportation of quantum states, and generation of four-photon Greenberger-HorneZeilinger entangled states. The production, control, and transceiving of states are all achieved in micrometer-scale silicon chips, fabricated by complementary metal-oxide-semiconductor processes. Our work lays the groundwork for scalable on-chip multiphoton technologies for quantum computing and communication.
Supplementary Information: Chip-to-chip quantum teleportation and
This supplementary section addresses chip-to-chip quantum teleportation and multi-photon entanglement in silicon.
- The section focuses on chip-to-chip quantum teleportation in silicon.
- The section also covers multi-photon entanglement in silicon.
- Together, these topics concern integrated silicon quantum-information experiments.
1 Device Details and Experimental Setup
The silicon device integrates microresonator photon sources, programmable interferometric operations, and coupling structures for creating, manipulating, and distributing photonic qubits. Its architecture supports up to four logical qubits and chip-to-chip quantum experiments.
- Device architecture: Up to four logical qubits are created and manipulated simultaneously in the integrated device.Photons are encoded in dual-rail modes and processed using programmable Bell projection and fusion operations.
- Device architecture: The MRR source array generates two photon pairs through spontaneous four-wave mixing, while MZIs and phase-shifters prepare and measure dual-rail qubits.
- Device design: The four MRRs are designed with 400 GHz free-spectral ranges, compatible with ITU channel spacing and off-the-shelf telecommunications instruments.
- Device design: The asymmetric MZI uses a 320 GHz free-spectral range to separate signal and idler photons selected three MRR free-spectral ranges from the pump.
- Fabrication and coupling: The silicon platform achieves approximately 2 dB/cm propagation loss and -0.8 dB peak grating-coupler loss at 1555 nm.The grating coupler has a 40 nm 1 dB bandwidth, and the 2×2 MMIs provide balanced splitting.
- Experimental setup: The experiment pumps the MRR array with 500 MHz, 15 ps pulses near 1550 nm at approximately 800 µW coupled power.Generated photons are coupled into fibers and filtered using wavelength-division multiplexers.
2 Micro-ring Resonator Single-photon Sources
The work develops silicon microring-resonator sources aimed at producing multiple indistinguishable heralded single-photons for scalable quantum processing. It characterizes source quality through spectral purity, photon-number purity, heralding efficiency, brightness, coincidence-to-accidental ratio, and photon indistinguishability.
- Source principles: Heralded single-photon sources generate signal photons when their paired idler photons are detected from spontaneous four-wave mixing.
- Source requirements: Scalable sources require high spectral purity, photon-number purity, heralding efficiency, brightness, and coincidence-to-accidental ratio.These metrics jointly characterize source quality, while spectral purity trades off with several other metrics.
- Source characterization: Photon indistinguishability is assessed by interfering heralded signal photons from two independent sources and measuring raw interference visibility.
- Source characterization: The MRR array provides near-identical resonance spectra, with a simulated theoretical spectral-purity limit of 92%.The characterization also measures brightness and CAR versus input power and shows brightness reduction from silicon nonlinear losses.
2.1 Resonant Enhancement of MRRs
Microresonator resonant enhancement supports bright, spectrally pure photon-pair generation and enables estimation of source quality from measured spectra, efficiencies, and count rates.
- Resonant enhancement: MRR resonant enhancement strengthens photon-pair generation while keeping photon-number purity close to unity and spectral purity near 92% for a basic design.Newer resonator designs are reported to promise spectral purity near unity.
- Source characterization: Nearly identical MRR resonance spectra are fitted to estimate linewidths, quality factors, and heralding efficiencies.The fitted parameters characterize spectral overlap and source performance across the array.
- Resonator model: The MRR model relates input and output fields to coupling, self-coupling, round-trip phase, and round-trip transmission.These parameters describe the resonator response used in the characterization.
- Efficiency estimation: Heralding efficiency is estimated from signal-idler detection and coincidence counts, while brightness data are fitted using count-rate models.The supplied passages define the measurement quantities but do not provide the full displayed fitting equations.
- Model limitations: Brightness estimation requires modification when non-PNR detectors, multipair emission, or nonlinear losses invalidate the low-power or single-pair assumptions.A more accurate rate equation is referenced for these practical conditions.
2.1 Resonant Enhancement of MRRs
The resonator source model accounts for nonlinear transmission losses and photon-number statistics when interpreting brightness, heralding, and multipair-emission measurements.
- Nonlinear losses: Signal and idler efficiencies are modified to include two-photon absorption and free-carrier absorption losses.The transmission factors are applied multiplicatively to the baseline channel efficiencies.
- Loss model: The nonlinear-loss model uses repetition rate, pulse width, resonator length, field enhancement, absorption coefficients, mode area, and free-carrier density.These parameters determine transmission through TPA and FCA.
- Measured brightness: Approximately 50 Mcts/s/mW^2 are generated inside the MRRs, while collected raw coincidences are approximately 20 kcts/s with CAR above 50 at 800 µW pump power.The reported operating point uses 15 ps pulses at a 500 MHz repetition rate.
- Photon-number statistics: Heralded second-order correlation measurements use ratios of two-fold and three-fold events to characterize multipair emission as a function of pump strength.The fitting model expresses multipair emission through higher-order terms of input pump power.
- Operating point: At 800 µW average pump power, the mean photon number per pulse is 0.065 after accounting for 1.25 dB input-to-MRR loss.The mean photon number is calculated from the power reaching the chip resonator.
2.2 Photon Indistinguishability Measurement (PIM)
Photon indistinguishability is assessed by interfering heralded photons from independent MRRs, while visibility is interpreted through spectral and photon-number purity.
- Measurement setup: Heralded single-photons from two independent MRRs are interfered after reconfiguring the chip for pairwise indistinguishability measurements.The circuit can be configured to compare any two MRR sources.
- Experimental caveat: Imperfect 50:50 MMI couplers distort the interference fringe but do not reduce raw MZI visibility.The imbalance prevents full transmission through the MZI while preserving the reported visibility behavior.
- Visibility interpretation: Spectral purity sets the maximum achievable visibility, whereas photon-number impurity lowers visibility as pump power increases.Losses reduce brightness but do not degrade raw visibility.
2.3 Effect of Spectral Separability On Interference
The paper links scalable multiphoton interference to spectrally separable, identical sources and analyzes how source matching preserves the coherence needed for entanglement.
- Scalable processing: Scaling the device requires pure, identical photon sources and high-fidelity multiqubit operators to coherently control up to four logical qubits.The device overlaps microring resonances and operates in a low-squeezing regime to improve spectral and number purity.
- Photon generation: Silicon SFWM generates degenerate, energy-conserved signal and idler photons through an inherent χ(3) nonlinear process.The joint spectral function describes frequency correlations between the produced photons.
- Bell-pair generation: Generating Bell pairs depends on high-visibility interference between photons from two MRR sources; without it, the reconstructed state becomes maximally mixed.The coherence terms of the density matrix vanish when the required interference is absent.
- Spectral matching: The interference condition requires tuning the sources so their joint spectral functions match, f(λs, λi) = f′(λs, λi).The text identifies identical single-photon sources as sufficient for this matching condition.
- Interference mechanism: Matching spectral contributions produce symmetric terms whose sum provides the quantum interference needed for the entangled state.The argument follows symmetry of the joint spectral integrals when f = f′.
2.3 Effect of Spectral Separability On Interference
The analysis distinguishes spectrally separable sources from correlated sources and shows that spectral correlations can suppress heralded quantum interference. Identical joint spectra alone are insufficient when signal and idler frequencies remain strongly correlated.
- Identical joint spectra: Identical joint spectral functions enable high-fidelity interference when source spectra are matched.The relevant condition is source-to-source spectral identity, not an assumption that the joint spectrum is uncorrelated.
- Spectral separability: Spectrally pure biphoton functions factor into independent signal and idler amplitudes, allowing perfect interference between photons from separate sources.The separability condition is f(λs, λi) = A(λs)B(λi).
- Spectral correlations: Correlated signal-idler photons produce orthogonal frequency terms that dominate the total state as the frequency dimension increases.Their ratio is given by limD→∞(D^2 − D)/D.
- Spectral correlations: Idler photons prevent factorisation of correlated terms and thereby prevent signal-photon interference.Unless the joint spectrum is extremely narrow, the overall state exhibits no interference.
- Spectral correlations: The correlated-source case yields a heralded MZI interference visibility of 33%.Visibility is defined as v = (cmax − cmin)/(cmax + cmin).
2.4 Locking Micro-ring Sources
The experiment stabilizes microring-resonator sources by tuning and locking their resonances. This maintains alignment across all four MRRs during the experiments.
- Resonance stabilization: Indistinguishable single-photons require precise tuning of the MRR resonances.Because the rings have identical free-spectral ranges, scanning one resonance can simultaneously match signal and idler overlap.
- Resonance stabilization: A weak fixed-frequency CW probe monitors each MRR output to correct unwanted resonance drift.Separate outputs contain light passing through individual MRRs for feedback control.
- Resonance alignment: A Lorentzian fit to the measured output intensity identifies the thermo-optic phase-shifter voltage required for resonance alignment.The minimum of the fitted line shape determines the required voltage.
- Resonance stabilization: All four MRR resonance positions remain well aligned throughout the experiments.The alignment is maintained over the whole experimental period.
3 Linear-optic Multi-qubit Operations
The silicon processor combines programmable single-qubit preparation and measurement with multi-qubit Bell and fusion operations. These circuits are tested through interference fringes, state tomography, and multi-photon measurements.
- Single-qubit operations: Mach-Zehnder interferometers and phase shifters independently control single-qubit phase and measurement probability amplitudes.Their combined action implements arbitrary single-qubit preparation and projective measurement across four qubits.
- Bell operation: The Bell operator decomposes into exchange, interaction, and exchange transformations that interfere photons from two qubits.The interaction includes Hadamard-like transformations implemented with MZIs.
- Bell operation: 80 ± 3% visibility is observed for the Bell-operation interference fringe, confirming coherent Bell entangling operation.The fringe is measured by rotating the input state and detecting qubits in the σxσx basis.
- Fusion operation: The fusion operator transmits photons in the |0⟩ mode and swaps photons in the |1⟩ mode for dual-rail qubits.Its action is mathematically analogous to a polarization beam splitter acting on polarization qubits.
- Fusion operation: 86 ± 4.0% visibility confirms the entangling fusion operation.The HOM-like fringe is measured while rotating the input state and detecting in the σxσx basis.
- Bell-state measurement: Bell-state measurements identify input states from coincidence events in specific qubit and mode combinations.For example, |Ψ+⟩ and |Ψ−⟩ produce distinct coincidence patterns.
4 Teleportation and Entanglement Swapping
The device generates, distributes, and teleports photonic qubit states within and between silicon chips. It also supports Bell-state distribution and chip-to-chip teleportation using path-polarization conversion.
- Teleportation: Quantum teleportation transfers a quantum state to another location through local state collapse and remote reconstruction using Bell states and Bell measurements.The protocol requires a shared entangled channel between the sender-side and receiver-side qubits.
- Intra-chip teleportation: The silicon device prepares arbitrary input states, generates an on-chip |Φ+⟩ channel, and applies a Bell measurement to teleport the state up to a local σx rotation.The Bell projection is performed between the input qubit and the channel qubit.
- Inter-chip distribution: The complete set of Bell states |Φ±⟩ and |Ψ±⟩ is distributed across two chips through path-polarization conversion and a 2-meter single-mode fiber.A fiber polarization controller compensates random polarization rotation in the fiber.
- Chip-to-chip teleportation: Chip-to-chip teleportation reconstructs |0⟩ and |1⟩ with fidelities of 0.940 ± 0.041 and 0.832 ± 0.048.The input is prepared on chip A, the fourth qubit is distributed to chip B, and tomography is performed on chip B.
- Significance: The work demonstrates chip-to-chip quantum teleportation as a capability relevant to quantum networks, quantum cryptography, and distributed quantum computing.The demonstration is described as proof of principle.
5 Generation, Certification, and Quantification of Genuine Multipartite GHZ Entangled States
The processor generates three- and four-photon GHZ states by applying a fusion operation to Bell pairs, then certifies genuine multipartite entanglement using witness and GME-concurrence measurements. Two-basis measurements reduce verification effort while still certifying multipartite entanglement.
- Generation of four-photon GHZ states: The fusion operator acts on signal photons from two Bell states to generate an on-chip four-photon GHZ state through post-selected four-fold coincidences.Photons 2 and 3 are fused from |Φ+⟩1,2 and |Φ+⟩3,4; detector events with one photon in each specified combination are retained.
- Generation of three-photon GHZ states: Measuring qubit 4 in the σx basis projects the four-photon state onto a three-photon GHZ state.The remaining photons are measured in the diagonal basis to generate the three-photon GHZ states.
- Entanglement swapping: Measuring qubits 2 and 3 in the σxσx basis swaps entanglement, leaving a Bell state between qubits 1 and 4.The fusion operator functions as a Bell analyser by projecting qubits 2 and 3 onto the Bell basis.
- Certification by entanglement witness: The entanglement witness is negative for genuine multipartite entangled states and positive for biseparable states, while GHZ-state certification uses population and coherence terms.The experiment estimates the witness and GHZ fidelity by measuring local observables with four on-chip projectors.
- GME-concurrence quantification: The three-photon state achieves CGME ≥0.390 ± 0.040, certifying multipartite entanglement for n = 3 by at least 9 standard deviations.The bound is obtained from four-fold coincidence measurements in the σz and σx bases, with Poissonian Monte Carlo error estimates.
- GME-concurrence quantification: The four-photon state achieves CGME ≥0.192 ± 0.039, certifying multipartite entanglement for n = 4 by at least 4 standard deviations.The calculation uses 30 diagonal density-matrix elements from σz and σx measurements, with errors estimated by Poissonian Monte Carlo simulation.
- Efficient certification: Two-basis measurement reduces GME verification to 2 global measurement settings, compared with 9 settings for full Bell-state tomography.For four- and three-photon GHZ states, the two-basis method uses 2 measurements, versus 5 and 4 for entanglement-witness verification, respectively.