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Entanglement Distillation between Solid-State Quantum Network Nodes
Norbert Kalb, Andreas A. Reiserer, Peter C. Humphreys, Jacob J. W. Bakermans, Sten J. Kamerling, Naomi H. Nickerson, Simon C. Benjamin, Daniel J. Twitchen, Matthew Markham, Ronald Hanson
TL;DR
Quantum networks need high-quality remote entanglement despite decoherence, photon loss, and imperfect control. This work distills entanglement between distant electron-nuclear solid-state nodes by generating, storing, and locally processing two remote states, yielding a heralded entangled output and a rate advantage over two-photon schemes.
Problem
Quantum networks require high-quality remote entanglement despite unavoidable errors, while prior distillation demonstrations lacked distant stationary memories or retained the distilled state only transiently.
Method
The experiment generates two single-photon-heralded remote states between communication qubits, swaps one into nuclear-spin memories, and applies local two-qubit operations for distillation.
Results
0.65(3) fidelity with the ideal Bell state, exceeding 0.5, demonstrates an entangled distilled state, while modeling shows fidelity surpasses both raw-state fidelities for larger θ.
Takeaways & Limitations
Generating, storing, and processing remote entangled qubits in one experiment provides a primitive for extended quantum networks and can speed entanglement generation.
Takeaways & Limitations
Direct tomography of raw states is capped at 0.5 because their unreferenced internal phase washes out coherences; stricter comparisons assume a perfectly known initial path-length difference.
Abstract
from arXiv · showhide
The potential impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable real-world imperfections necessitate means to improve remote entanglement by local quantum operations. Here we realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit nodes. We demonstrate the heralded generation of two copies of a remote entangled state through single-photon-mediated entangling of the electrons and robust storage in the nuclear spins. After applying local two-qubit gates, single-shot measurements herald the distillation of an entangled state with increased fidelity that is available for further use. In addition, this distillation protocol significantly speeds up entanglement generation compared to previous two-photon-mediated schemes. The key combination of generating, storing and processing entangled states demonstrated here opens the door to exploring and utilizing multi-particle entanglement on an extended quantum network.
GENERATION AND DISTILLATION OF REMOTE ENTANGLED STATES
The experiment realizes entanglement distillation between two distant solid-state two-qubit nodes. Two probabilistically generated remote states are stored across communication and memory qubits, then processed locally to produce a higher-quality state.
- Photon detection heralds a raw entangled state on the communication qubits, which is swapped onto the memories before generating a second raw state.
- Two nodes separated by two meters each use a communication qubit for remote entanglement and a memory qubit for storage.
- The protocol applies local operations and classical communication to several lower-quality shared states to distill a higher-quality remote state.
- Single-photon-based entangling, nuclear-spin storage, and real-time feedback support the demonstrated network primitive.
- The protocol increases entanglement-generation efficiency relative to earlier two-photon-coincidence schemes and removes optical path-length dependence from stand-alone single-photon protocols.
QUANTUM NETWORK NODES
The network nodes combine NV electron-spin communication qubits with nearby nuclear-spin memories and implement the local gates needed for distillation. Tomography confirms high-fidelity local entangled-state preparation at both nodes.
- Each node uses an NV electron spin in diamond as a communication qubit and a nearby carbon-13 nuclear spin as a memory qubit.
- The two diamond-chip nodes operate in separate 4 K cryostats separated by two meters.
- Universal nuclear-spin control through hyperfine-coupled dynamical-decoupling gate sequences supplies the toolbox for all four distillation steps.
- The compiled circuit reduces local-gate overhead by implementing the SWAP with two conditional gates for initialized memories.
- 0.96(1) and 0.98(1) are the measured Bell-state fidelities for nodes A and B, respectively.
ROBUST STORAGE OF QUANTUM INFORMATION
The memories must preserve quantum information while communication qubits undergo an unknown number of probabilistic entangling attempts. Real-time phase feedback compensates attempt-dependent shifts, enabling faithful storage over hundreds of attempts.
- Probabilistic entanglement generation requires memory storage during an a priori unknown number of attempts.
- Failed attempts trigger stochastic communication-qubit repumping, whose interaction with the memory can cause dephasing.
- Real-time feedback compensates deterministic memory phase-shifts while preserving the communication qubit holding the second raw copy.
- 273(5) and 272(4) entangling attempts are the 1/e decay values for dephasing-sensitive memory states in nodes A and B, respectively.
- Energy eigenstates remain highly faithful, while phase-sensitive superposition states decay during repeated entangling attempts.
EXPERIMENTAL ENTANGLEMENT DISTILLATION
The full protocol generates two remote raw states, stores the first, and heralds distillation through local gates and measurement. Its design tolerates correlated dephasing and uses feedback and bounded attempts to preserve storage and data rate.
- Single-photon detection after beam-splitter interference heralds each raw remote state generated from the communication qubits.
- The first raw state is swapped onto the memories, freeing the communication qubits for a second remote-state generation round.
- The readout combination (0A,0B) heralds successful distillation, with unnormalized branch traces representing occurrence probabilities.
- The final Bell-state phase is determined by whether the photons were detected in the same or different output ports.
- Correlated dephasing of the raw states is tolerated, leaving sensitivity only to optical path-length drifts within an individual protocol run.
- Automatic resonance feedback and attempt bounds produce event rates of around 10 Hz when two remote states are successfully generated.
DISTILLATION RESULTS
The protocol produces a distilled entangled state whose fidelity exceeds relevant raw-state fidelities under suitable conditions, while measured fidelity reaches 0.65(3). Modeling attributes remaining limits mainly to memory and control errors and imperfect photon indistinguishability.
- Measured distillation: 0.65(3) fidelity with the ideal Bell state exceeds 0.5, proving entanglement in the distilled state.The density matrix also has high populations only in the Bell-state subspace, indicating reduced separable admixture.
- Fidelity comparison: The experiment compares the distilled state separately with memory-held and communication-qubit raw states because imperfections make the two raw states different.Swap and storage errors affect the memory state, while short-timescale path variations affect the communication state.
- Experimental limitation: Direct tomography of raw states cannot exceed 0.5 because an unreferenced internal phase washes out coherences through optical path-length variations.Future optical path stabilization may make the internal phase accessible.
- Measured distillation: Figure 4A reports 0.65(3) fidelity for both detector-signature outcomes at θ = π/6 with at most 50 second-round attempts.The two outcomes are different detectors clicking and the same detector clicking twice.
- Fidelity comparison: For larger θ, the distilled-state fidelity significantly surpasses both raw-state fidelities, demonstrating entanglement distillation.For small θ, gains are offset by errors from the additional distillation operations.
- Error analysis: The model agrees with measured fidelities across separable admixtures and attempt numbers, identifying memory dephasing, control errors, and two-photon distinguishability as main limits.Measured two-photon interference visibility is 0.73(3), and the effect occurs twice during distillation but once during raw-state generation.
EBIT RATE
The distillation protocol achieves a higher entangled-bit generation rate than the modeled two-photon-coincidence protocol under identical experimental conditions. Its ideal success probability scales linearly rather than quadratically with photon-detection probability, despite added local-operation overhead.
- Rate mechanism: For typical pdet ≈ 10^-3, distillation has a rate advantage because its ideal success probability scales linearly with pdet rather than pdet^2.This advantage can outweigh the overhead of additional local quantum logic.
- Rate comparison: The ebit rate is upper-bounded as r = νE_N using the success rate ν and logarithmic negativity E_N.Figure 5 compares this rate for distillation and the Barrett-Kok protocol as a function of excitation angle θ.
- Rate comparison: The distillation protocol outperforms the Barrett-Kok two-photon-coincidence protocol under identical experimental conditions.The advantage remains both with measured two-photon indistinguishability and in the idealized comparison excluding those imperfections.
CONCLUSION AND OUTLOOK
Combining remote-entanglement generation, storage, and processing provides a primitive for extended quantum networks. The demonstrated protocol also counters distributed decoherence and can speed entanglement generation across related platforms.
- Conclusion: Combining generation, storage, and processing of remote entangled qubits provides a universal primitive for extended quantum networks.The protocol is presented as a method to counter unavoidable decoherence during entanglement distribution.
- Outlook: The protocol’s entanglement-generation speedup can be harnessed in other solid-state defect centers and trapped-ion platforms.Proposed improvements include protected encodings, longer dephasing times, faster resets, and photonic cavities.
- Outlook: Recent multiqubit-control and quantum-error-correction techniques are compatible with the experiment, supporting scaling to more qubits and broader network functionality.The outlook identifies these techniques as relevant to near-term extension of the network.