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Experimental demonstration of memory-enhanced quantum communication
Mihir K. Bhaskar, Ralf Riedinger, Bartholomeus Machielse, David S. Levonian, Christian T. Nguyen, Erik N. Knall, Hongkun Park, Dirk Englund, Marko Lončar, Denis D. Sukachev, Mikhail D. Lukin
TL;DR
The work addresses constraints on extending quantum-memory operation while preserving asynchronous Bell-state measurement performance. It characterizes and optimizes the memory-assisted protocol, achieving a 3.8±1.1-fold secret-key-rate excess over the conventional limit p/2 at a 1.2 MHz clock rate.
Problem
Short microwave π pulses cause additional decoherence from ohmic heating, constraining usable memory time and pulse-sequence length.
Method
The experiment uses asynchronous Bell-state measurements with a spin memory, estimating QBER across basis combinations and optimizing mean photons per memory pulse and pulse number.
Results
3.8±1.1-fold secret-key-rate excess over the conventional limit p/2 was achieved at a 1.2 MHz clock rate, with optimal performance near N ≈124 and 69 dB effective channel loss.
Takeaways & Limitations
The measured configuration is competitive with a standard MDI-QKD system operating at 4.5+1.3 −1.2 MHz clock rate.
Takeaways & Limitations
Ohmic heating from short microwave pulses limits pulse sequences to Nπ = 128 and usable memory time to approximately 20 µs.
Abstract
from arXiv · showhide
The ability to communicate quantum information over long distances is of central importance in quantum science and engineering. For example, it enables secure quantum key distribution (QKD) relying on fundamental principles that prohibit the "cloning" of unknown quantum states. While QKD is being successfully deployed, its range is currently limited by photon losses and cannot be extended using straightforward measure-and-repeat strategies without compromising its unconditional security. Alternatively, quantum repeaters, which utilize intermediate quantum memory nodes and error correction techniques, can extend the range of quantum channels. However, their implementation remains an outstanding challenge, requiring a combination of efficient and high-fidelity quantum memories, gate operations, and measurements. Here we report the experimental realization of memory-enhanced quantum communication. We use a single solid-state spin memory integrated in a nanophotonic diamond resonator to implement asynchronous Bell-state measurements. This enables a four-fold increase in the secret key rate of measurement device independent (MDI)-QKD over the loss-equivalent direct-transmission method while operating megahertz clock rates. Our results represent a significant step towards practical quantum repeaters and large-scale quantum networks.
EXPERIMENTAL SETUP
The experiment uses a millikelvin nanophotonic cavity QED platform containing SiV centers, with optical interrogation through fiber and microwave control hardware.
- Measurements are performed in a dilution refrigerator with a 20 mK base temperature and a superconducting vector magnet.The setup also includes cryogenic microscopy, piezo positioners, and fiber and microwave feedthroughs.
- The SiV–cavity system is optically interrogated through a fiber network without free-space optics.
Experimental implementation of asynchronous BSM
The asynchronous Bell-state measurement requires synchronized optical and microwave timing together with interferometrically stable analysis of reflected time-bin qubits.
- A single HSDIO synchronizes equipment generating microwave and optical fields for precise pulse timing.
- A narrow-linewidth Ti:Sapphire laser generates photonic qubits and locks the time-delay interferometer used for heralding.Reflected photons pass through the interferometer and are detected by SNSPDs.
- The interferometer is passively stabilized and actively re-locked about every 200 ms to compensate thermal drift.A 1.8 MHz frequency shift enables X-basis measurements, while fiber polarization controllers address polarization sensitivity.
- A preselection procedure initializes the SiV spin and monitors reflected-count thresholds to maintain resonance with the photonic qubits.
Calibration of fiber network
The fiber network routes photons to and from the memory while calibration quantifies coupling, transmission, detector efficiency, and total heralding efficiency.
- Photons enter through the lossy 1% port of a 99:1 beamsplitter and reflected photons return through its efficient 99% port.The beamsplitter loss is included in the estimated channel loss for benchmarking.
- The high-level sequence uses HSDIO feedback and automatic re-locking, while the main sequence repeats its first step 4000 times and limits readout to ∼1 MHz.
- The schematic includes arbitrary waveform generation, time-tagging, fiber delivery and collection, polarization control, and phase-locked optical-field preparation.
- The cavity’s spin-dependent reflectivity gives an average device reflectivity of ηsp = 0.493.The |↑⟩ state reflects 94.4% of incident photons, whereas |↓⟩ reflects 4.1%.
- Two independent calibration methods estimate the total heralding efficiency as η = 0.425 ± 0.008 and η = 0.422 ± 0.005.
- The reported average heralding efficiency is η = 0.423 ± 0.004, obtained from the two calibration techniques.
CHARACTERIZATION OF THE NANOPHOTONIC QUANTUM MEMORY.
The nanophotonic memory combines a strongly coupled SiV–cavity system with microwave-controlled spin coherence suitable for time-bin asynchronous measurements.
- The spin transition is split by a nearby 13C, and 32 ns microwave π pulses address both transitions equally.This pulse duration balances temporal multiplexing against microwave-heating effects.
- XY8-1 dynamical decoupling extends spin coherence beyond 200 µs.For BSM experiments, the 142 ns time-bin spacing decouples the spin from the nearby 13C, although coherence decreases at large pulse numbers because of heating.
THEORETICAL DESCRIPTION OF ASYNCHRONOUS BELL STATE MEASUREMENT
The protocol stores Alice’s photon state in a spin memory, then combines it with Bob’s asynchronously arriving photon to perform a Bell-state measurement. Spin readout and detection outcomes reveal input correlations without revealing the individual photon states.
- Protocol operation: The critically coupled cavity reflects photons conditionally on the SiV spin state, enabling a Bell-state measurement between asynchronously arriving photons.Only two of four Bell states are accessible at a time because the others are transmitted through the cavity and lost.
- Protocol operation: A π/2 pulse prepares the spin, while dynamical-decoupling π pulses preserve its state when no photon arrives.Alice’s reflected time-bin qubit entangles with the spin during reflection.
- Protocol operation: Measuring Alice’s reflected photon in the X basis teleports her state onto the spin, with m1 recording the detection outcome.The spin then stores Alice’s photonic state during the decoupling sequence.
- Protocol outcomes: The three measurement outcomes have individually random signs, but their total parity identifies whether valid X- or Y-basis inputs were the same or opposite.For Y-basis inputs, Alice and Bob adjust the sign using timing information about Charlie’s microwave pulses.
- Protocol outcomes: The protocol also supports inputs sent in different bases when their phases satisfy φ1 + φ2 = 0, allowing their correlations to be inferred.This extends the usable input configurations beyond pairs that are both in the X or Y basis.
Test of Bell-CHSH inequality
The experiment tests correlations produced by the asynchronous BSM using Bell-CHSH measurements on selected input-state pairs. The reported analysis compares input correlations conditioned on positive and negative parity outcomes against the Bell-CHSH bound.
- Experimental test: Input photons are sampled equally from the X, Y, a, and b states, with cases selected where the inputs are 45° or 135° apart.The selected pairs are evaluated conditioned on the BSM parity outcome.
- Experimental test: The Bell-CHSH parameter combines four input-correlation terms and is bounded by 2 for the tested correlations.The terms correspond to the xa, xb, ya, and yb basis combinations.
- Measurement basis: Time-bin qubit measurements use early and late detection peaks for Z-basis states and the central overlap bin for X-basis interference.The figure passage describes the measurement signatures in the time trace.
- Results: The asynchronous BSM truth table lists the parity outcome for each valid Alice–Bob input-state pair.For Y inputs, the sign is adjusted according to whether the timing corresponds to an even or odd free-precession interval.
- Results: The individual input-correlation terms are plotted separately for positive and negative parity outcomes.The supplied description specifies the comparison but does not state the measured Bell-CHSH values.
Estimation of QBER
The analysis estimates QBER and secret-key performance while balancing photon number, multiplexing, memory coherence, and device heating. It identifies operating conditions that maximize memory-assisted communication relative to direct transmission.
- QBER estimation: The average QBER is inferred from balanced input probabilities and posterior likelihoods across the relevant basis combinations.The final unbiased QBER posterior combines the XX and YY contributions and incorporates statistical and systematic uncertainty.
- Secret-key estimation: Secret-key fractions are calculated from mutual-information bounds against individual eavesdropper attacks, using the full QBER posterior for uncertainty estimates.The resulting uncertainties propagate to the extracted secret-key rates.
- Optimization: Undetected third-photon scattering increases QBER as ⟨n⟩m rises, while the memory’s finite heralding efficiency limits the associated fidelity.The experiment therefore operates near ⟨n⟩m ≲ 0.02, where further reduction does not significantly improve performance.
- Optimization: N can increase the number of photonic qubits per memory initialization, but bandwidth and coherence constraints limit multiplexing.Microwave heating at large N introduces additional errors and restricts the usable memory time.
- Results: The memory-based sifted-key rate exceeds the ideal direct-transmission MDI-QKD capability because of high heralding efficiency and many photonic qubits per memory time.The comparison uses the theoretical direct-transmission upper bound and measurements across N values including 504.
- Results: The optimal operating point is ⟨n⟩m ∼ 0.02 and N ≈ 124, corresponding to 69 dB effective loss or roughly 350 km of telecommunications fiber.At this point, BSM successes occur at roughly 0.1 Hz.
- Limitations: Imperfect preparation of photonic qubits is identified as another limitation on QBER and communication-link performance.The preparation uses phase patterns generated by an optical AWG and phase modulator, with finite-bandwidth amplification contributing to imperfection.
- Results: At N = 248, the effective clock rate is 1.2 MHz, and the secret-key rate exceeds the conventional p/2 limit by 3.8 ± 1.1.The passage compares this configuration with a standard MDI-QKD system operating at 4.5+1.3 −1.2 MHz.
Performance of memory-assisted MDI-QKD
The asynchronous Bell-state measurement device is evaluated per channel use in an optimized regime, with measured QBER and key-rate enhancements compared against direct-transmission and relevant bounds.
- N = 124 and ⟨n⟩m ≲0.02 define the device’s optimal operating regime.This regime is used to characterize performance across datasets.
- 0.116 ± 0.002 is the average QBER for combined N = 124 datasets below ⟨n⟩m ≲0.02.The main-text key-rate dataset has QBER 0.110 ± 0.004 at ⟨n⟩m ≈0.02.
- The enhancement in sifted key rate is independent of ⟨n⟩m when Nπ, Nsub, and therefore N = NπNsub are fixed.At low ⟨n⟩m, negligible three-photon events cause QBER and secret-key-rate enhancement to saturate.
- Performance is summarized on per-channel-use and per-channel-occupancy bases, with comparisons to ideal MDI-QKD and repeaterless bounds.These comparisons are reported in Table S4.
- A 99:1 biased-basis extrapolation can enhance secret key rates by at most a factor of 2.Biased input bases reduce channel uses when Alice and Bob send photons in different bases while remaining compatible with secure key distribution.