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Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity
Kejin Wei, Nora Tischler, Si-Ran Zhao, Yu-Huai Li, Juan Miguel Arrazola, Yang Liu, Weijun Zhang, Hao Li, Lixing You, Zhen Wang, Yu-Ao Chen, Barry C. Sanders, Qiang Zhang, Geoff J. Pryde, Feihu Xu, Jian-Wei Pan
TL;DR
Exponential quantum-classical gaps are proven for communication complexity, while the quantum switch has been proposed as a way to achieve exponential advantage through a superposition of communication directions. This experiment implements a switch-based one-way distributed computation with a photonic qudit target, and reports communication below 69.6% of the minimum for causally definite quantum protocols.
Problem
Communication complexity studies how separated parties can compute with minimal communication, and quantum communication tasks admit proven exponential gaps over classical protocols.
Source: p. 2Method
The experiment implements a quantum switch with a qubit control and a d-dimensional photonic qudit target, encoding control in path and target in photon arrival time.
Source: pp. 3–4Results
69.6 ± 0.6%: the protocol transmits this fraction of the information required by any causally definite quantum protocol.
Source: p. 8Takeaways & Limitations
The results elucidate the crucial role of communication-direction coherence in the exponential separation for a one-way distributed processing task.
Source: p. 10The temporal-qudit encoding is not efficiently scalable to very large n because the required number of time bins grows exponentially with target-qubit count.
Source: p. 10
Abstract
from arXiv · showhide
Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication complexity. Recently, a novel quantum resource called the quantum switch---which creates a coherent superposition of the causal order of events, known as quantum causality---has been harnessed theoretically in a new protocol providing provable exponential separation. We experimentally demonstrate such an advantage by realizing a superposition of communication directions for a two-party distributed computation. Our photonic demonstration employs $d$-dimensional quantum systems, qudits, up to $d=2^{13}$ dimensions and demonstrates a communication complexity advantage, requiring less than $(0.696 \pm 0.006)$ times the communication of any causally ordered protocol. These results elucidate the crucial role of the coherence of communication direction in achieving the exponential separation for the one-way processing task, and open a new path for experimentally exploring the fundamentals and applications of advanced features of indefinite causal structures.
Appendix A: Comparison of our protocol with that of Ref. [16]
The experiment modifies the protocol of Ref. by using a different, more readily realizable definition of X(x). Its target dimension is one qubit larger than in the original scheme, but this is not inherent to time-bin encoding.
Appendix A: Comparison of our protocol with that of Ref. [16]
- The implemented X(x) adds x modulo 2^(n+1), rather than using modulo-two addition as in Ref..The modified permutation retains the property [X(x), X(y)] = 0 for all x and y, while being more readily realizable experimentally.Source: Appendix A · p. 11
- The target system uses n+1 qubits instead of the n qubits in Ref., but this is not a fundamental consequence of time-bin implementation.An n-qubit target is possible with a permutation modulo 2^n, using fast switches in addition to delays.Source: Appendix A · p. 11
- The alternative circuit for X(x) uses fast switches in addition to delays.The text points to Fig. 5 for this implementation.Source: Appendix A · p. 11
Appendix B: Practical considerations
The single-photon encoding limits loss exposure to one photon, but its time-bin representation requires exponentially more bins as the target-qubit count grows. The source coherence length also cannot span the interferometer in this setup.
Appendix B: Practical considerations
- Encoding the multi-qubit system in one photon limits the system to the probabilistic loss associated with a single photon.Loss increases communication because it requires protocol repetition, while the benchmark is against optimal lossless causally ordered protocols.Source: Appendix B · p. 11
- The time-bin encoding requires exponentially more bins as the target-qubit count grows, practically limiting scalability to arbitrarily high n.The authors nevertheless report reaching a regime where the causally indefinite protocol outperforms any causally definite protocol.Source: Appendix B · p. 11
- Using a single photon makes the rule that each party receives one system unambiguous, unlike a coherent state split into components that could count as two systems.The authors contrast their approach with earlier communication-complexity experiments using coherent states.Source: Appendix B · pp. 11–12
- The source coherence length is several centimeters and does not cover the switch; a longer length is unsuitable for this setup.The interferometer path is long, while time-bin modulation requires coherence length shorter than the bin separation.Source: Appendix B · p. 12
- An indefinite causal order has also been formally witnessed without an especially narrowband single photon.Source: Appendix B · p. 12
1. Heralded single-photon source
The heralded source uses type-II spontaneous parametric down-conversion to produce photon pairs, then detects one photon to herald its correlated partner. The reported heralding efficiency is approximately 62%.
1. Heralded single-photon source
- A 780-nm continuous-wave laser pumps a 10 mm PPKTP crystal, producing orthogonally polarized photon pairs at 1560 nm through type-II spontaneous parametric down-conversion.Source: §1 · p. 12
- One down-converted photon is detected by SNSPD1 to herald its correlated photon, with 80.6% detection efficiency.The photons are coupled into single-mode fibers with 76.9% coupling efficiency.Source: §1 · p. 12
- The heralding efficiency is approximately (62.0 ± 1.0)%, including photon-pair source setup losses but excluding protocol implementation elements.Source: §1 · p. 13
2. Sagnac loop
The Sagnac loop uses a beam splitter to create a superposition of communication directions and lets Alice and Bob apply input-dependent unitaries to the photon. The paths then interfere before detection.
2. Sagnac loop
- A 50:50 beam splitter creates the superposition of communication direction in the Sagnac loop.Source: §2 · p. 13
- Alice and Bob implement input-dependent unitaries using phase modulators and variable delays as the photon visits their stations.Because f(0) = g(0) = 0 and the photon starts in the first time bin, the first station applies only delays.Source: §2 · p. 14
- After the stations, the photon traverses a 7 km fiber spool, the paths interfere at the beam splitter, and SNSPDs register detections.Source: §2 · p. 14
3. Dark counts
The causally indefinite protocol has a coincidence window of 2n+2 ns for 2 ns time bins, increasing exposure to dark counts; low-dark-count SNSPDs are used to suppress them.
3. Dark counts
- 2n+2 ns is the coincidence window for 2 ns time bins, about (n + 1)/3 orders of magnitude larger than in normal two-photon detection.The heralded photon can occupy one of 2n+1 time bins while the heralding photon arrives in a given bin.Source: §3 · p. 14
- A dark count during the window, or a gated subset of it, can be registered erroneously as an event.Source: §3 · p. 14
- Two SNSPDs with dark-count rates below 10 Hz and detection efficiency above 72.5%, plus a low-loss bandpass filter, suppress thermal-background dark counts.Source: §3 · p. 14
4. Losses
The setup minimizes loss across photon generation, the Sagnac loop, and detection to reduce experimental communication requirements.
4. Losses
- 11.62 dB is the overall system loss, excluding the variable delays in Alice’s and Bob’s stations.Source: §4 · p. 15
- (62.0 ± 1.0)% heralding efficiency corresponds to 2.07 dB source loss, achieved with optimized beam waists and a high-quality heralding SNSPD.Source: §4 · p. 15
- Custom low-loss Sagnac-loop components and SC/PC-to-FC/PC mating sleeves reduce connector loss to below 0.11 dB, versus about 0.3 dB for FC/PC-to-FC/PC sleeves.Source: §4 · p. 15
- The detection SNSPDs have efficiencies of 72.0% and 76.5% and dark-count rates of 8.3 Hz and 9.3 Hz, respectively.Source: §4 · p. 15
- The beamsplitter balancing loss is 0.27 dB.Source: §4 · p. 15
5. Measurement of the second-order correlation function
The experiment measures the heralded source’s second-order correlation at zero delay to verify single-photon operation, finding a value close to zero.
5. Measurement of the second-order correlation function
- The g(2)(0) measurement tests the assumption that a pure single photon enters the Sagnac loop, with an ideal source giving g(2)(0) = 0.Source: §5 · p. 15
- The calculation uses C1 for SNSPD1 singles, C12 and C13 for two-fold coincidences with SNSPD2 and SNSPD3, and C123 for three-fold coincidences.Source: §5 · p. 15
- g(2)(0) = (3.27±23.5)×10^-5 at 3 mW pump power, consistent with an almost perfect single-photon source.Count rates were averaged over 5 minutes; error bars are one standard deviation under Poisson statistics.Source: §5 · p. 16
- The near-zero result implies that Alice’s and Bob’s hypothetical output-port counters would each register one channel use.Source: §5 · p. 16
6. Implementation of the unitary transformations
The implementation realizes input-dependent delays with fiber segments and calibrates them precisely so phase modulation lands within the intended time bin.
6. Implementation of the unitary transformations
- Each party’s n fiber segments provide 2n possible delays, with the k-th segment’s two fiber options differing by 2^(k−1) time bins.A 25 GHz waveform generator supplies 2 ns modulation pulses, timed to place the photon in the first bin’s middle.Source: §6 · p. 16
- The home-built photon-counting OTDR measures segment delays at 1 ps resolution, addressing the inadequate sensitivity of a conventional OTDR.Commercial-spool OTDR uncertainty is stated as ±(3.75+0.001×L/v) ns; home-made segments reach about 2.5 ps uncertainty.Source: §6 · pp. 16–17
- Fiber options are selected to create the required delays, and connectorized segments are polished with SC/FC connectors to achieve low insertion loss.Source: §6 · pp. 16–18
- The fiber-segment choices implementing X(x) are illustrated in Fig. 6.Source: §6 · p. 16, Figure 6 · p. 17
- The delay-measurement setup is illustrated in Fig. 7.Source: Figure 7 · p. 17
- For combinations of fiber segments, the largest delay deviations are 101 ps for Alice and 46 ps for Bob, both below the 900 ps tolerance for applying the phase in the desired bin.Source: §6 · p. 18
Appendix D: Detailed Experimental results
The appendix reports complete experimental results and plots error probabilities for system sizes n = 11 to 9. Errors rise with system size, possibly because thermal expansion causes uncompensated length mismatch.
Appendix D: Detailed Experimental results
- Figure 8 plots experimental error probabilities for system sizes ranging from n = 11 to 9.Table II contains the complete experimental results.Source: Appendix D · p. 18
- The worst-case error probability is the largest for each system size, and error bars represent 1 standard deviation.Source: Appendix D · p. 18
- Thermal expansion may cause uncompensated length mismatch as n grows, offering a possible reason for rising error probabilities.Source: Appendix D · p. 18