Distributed Quantum Superiority Experiment

• Distributed quantum superiority is a framework where spatially separated nodes share entanglement to achieve precision scaling and computational tasks beyond classical shot-noise limits.
• The experiment employs combined parallel and multi-pass entanglement strategies, utilizing GHZ states and sequential phase encoding to realize measurable improvements in phase estimation.
• Experimental implementations report up to 4.7 dB sub-shot-noise enhancement in distributed metrology, validating scalable network architectures and benchmarks against optimal classical models.

A distributed quantum superiority experiment is defined as a multipartite quantum-information or metrological protocol implemented over spatially separated nodes or sensors, in which entanglement and/or other nonclassical resources enable a measurable and operationally relevant performance advantage unattainable by any classical or even more general probabilistic theory under identical constraints. Distributed superiority encompasses both sensing (distributed quantum metrology) and distributed computing/communication, provided the demonstration is based on a scalable, physically plausible network architecture and benchmarks are drawn from optimal classical or general probabilistic strategies of matching resource profile.

1. Fundamental Quantum Bounds and Networked Strategies

In distributed quantum metrology, the principal benchmarks are the shot-noise limit (SNL) and the Heisenberg limit (HL). For estimating a phase or a linear combination of phases, the SNL represents the best possible precision with classical or independent probes: $\Delta\phi_{\rm SNL} \sim 1/\sqrt{N}$ where $N$ is the number of independent photon-passes or particles interrogating spatially distributed parameters. In contrast, quantum entanglement enables Heisenberg scaling,

$\Delta\phi_{\rm HL} \sim 1 / N$

which is attainable with maximally entangled Greenberger–Horne–Zeilinger (GHZ) states or optimal mode-particle entangled probes, as established in "Distributed quantum phase estimation with entangled photons" (Liu et al., 2021).

Quantum networks realize distributed superiority via:

• Parallel mode entanglement: GHZ-like states spanning multiple modes/sensors such that a global linear phase function accumulates enhanced sensitivity.
• Multi-pass (sequential) strategies: Individual photons undergo multiple traversals through local phase-shifters, exploiting temporal or spatial mode-reuse.
• Combined parallel+multi-pass strategies: Maximizing total photon-pass budget with distributed entanglement per sensor and per photon, as in "Distributed quantum phase estimation with entangled photons" (Liu et al., 2021).

Analogously, in distributed quantum information processing, quantum gate teleportation or DCLC (distributed computing with limited communication) scenarios harness nonlocal entanglement to outperform all classical decomposable strategies (Main et al., 2024, Saha et al., 2020).

2. Pioneering Distributed Quantum Superiority Demonstrations

The first laboratory certification of distributed quantum superiority in metrology was achieved by Liu et al., combining spatially distributed six-photon entanglement, parallel and sequential interrogation, and explicit violation of SNL by measurable dB margins (Liu et al., 2021). Their benchmarks included:

• Single-mode two-photon GHZ protocols: Achieving up to 1.44 dB below SNL.
• Three-mode entangled protocols: Averaged phase estimation with error 2.7 dB below SNL.
• Six-mode, multi-pass combined protocols: Realizing 4.7 dB improvement over SNL with 21 effective photon-passes.

A distinct milestone was the field demonstration without post-selection, featuring high-heralding-efficiency, entangled photon sources over 240 m (and 10 km) optical fiber baselines, and demonstrating an unconditional 0.916 dB violation of SNL (Zhao et al., 2020).

In distributed computing, explicit protocols based on pre-shared bipartite entanglement, one quantum message per node, and a Bell measurement at a referee site, solve “dual-layer” nontrivial tasks (XOR/XNOR function composition) with perfect success—a feat impossible for any classical or even generalized probabilistic theory with identical communication constraints (Saha et al., 2020).

3. Experimental Implementations and Measured Metrics

Distributed quantum superiority experiments are characterized by:

• Entangled-photon sources: Ultrafast pulsed-laser-driven spontaneous parametric down-conversion to yield near-ideal Bell or GHZ states distributed among spatially separated optical modes (Liu et al., 2021).
• Phase encoding and multi-pass delays: Implementation of distributed phase functions via phase-shifter arrays, Hong–Ou–Mandel interferences, and delay-line optics for photon re-injection.
• Detection and analysis: Photon-number-resolving, high-efficiency superconducting nanowire detectors; measurement in product or global entangled bases; explicit computation of Fisher information and error reduction.
• Field deployment: Source and sensor separation by hundreds of meters to tens of kilometers in optical fiber, with unconditional analysis including all detection events (no post-selection) (Zhao et al., 2020).

Performance is quantified by Fisher information ($F$), root-mean-square estimation error, and dB improvement over SNL: $$\text{Improvement (dB)} = 20 \log_{10}\left(\frac{\Delta\phi_{\rm SNL}}{\Delta\phi_{\rm exp}}\right)$$ Sub-SNL dB levels directly certify quantum superiority in the distributed sensing context.

4. Comparison to Classical and Probabilistic Benchmarks

Optimal classical strategies (shot-noise-limited, separable-probe benchmarks) and generalized probabilistic (GPT) models lacking entanglement cannot achieve perfect success in distributed nontrivial tasks under the same quantum-limited communication constraints (Saha et al., 2020). In metrology, no separable mode-particle probe yields sub-SNL precision at fixed total photon-pass budgets (Liu et al., 2021). In communication and computation, the operational dimension of classical or GPT messages bounds success probabilities away from 1 for nontrivial dual-layer tasks, highlighting the exclusivity of quantum strategies.

Table 1: Comparison of Distributed Superiority Protocols

Domain	Quantum Advantage Metric	Classical/GPT Bound	Experimental Demonstration
Metrology	SNL violation (dB)	Max SNL precision	(Liu et al., 2021, Zhao et al., 2020)
Communication/DCLC	P_success=1	P_classical^* < 1	(Saha et al., 2020)
Computing/Gate-Teleportation	Gate/process fidelity, universal nonlocal gates	No deterministic nonlocal gates	(Main et al., 2024)

5. Scalability, Network Architectures, and Future Directions

Foundational superiority has expanded to distributed computing, including deterministic non-local gate teleportation over photonic links between spatially separated ion-trap modules (Main et al., 2024) and distributed implementations of noise-reducing shallow quantum algorithms (e.g., Grover’s search, Simon’s algorithm) across multiple QPUs (Avron et al., 2021). Modular architectures enable scaling via photonic or fiber-optic interfaces and entanglement purification schemes.

Recent theoretical and simulation advances show the feasibility of distributed quantum error correction and circuit-level superiority even when inter-node entanglement rates are up to five times slower than local gate operations. Distributed partial error correction (CliNR) protocols executed on ring-topology QPU arrays can outperform monolithic implementations in both logical error rate and execution time, demonstrating the regime of distributed quantum superiority for near-term, slow-interconnect, multi-QPU devices (Dobbs et al., 11 Dec 2025).

Distributed quantum superiority heralds applications in:

• Quantum-enhanced sensor arrays for time, frequency, and field metrology.
• Large-scale modular quantum computation and secure multiparty cryptographic tasks.
• Operational discrimination of quantum theory from general probabilistic theories via distributed communication complexity benchmarks.

6. Outlook and Open Challenges

Experimental progress has made distributed quantum-superior protocols technically attainable both in laboratory and field conditions. Key ongoing challenges include scaling to higher numbers of network nodes; integrating quantum repeaters and error correction; increasing detection efficiency and entanglement fidelity; and realizing practical distributed algorithms of complexity beyond shallow search or parameter estimation.

The field continues to push the boundary of what is possible at network-level resource-constrained quantum architectures, establishing distributed quantum superiority as both an empirical fact and a rigorous theoretical milestone (Liu et al., 2021, Zhao et al., 2020, Saha et al., 2020, Main et al., 2024, Avron et al., 2021, Dobbs et al., 11 Dec 2025).