Quantum

Experimental demonstration of quantum advantage in communication complexity for Euclidean distance problem

Verena Yacoub, Niraj Kumar, Iordanis Kerenidis, Eleni Diamanti

Featured June 2, 2026

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Simply

Using special light pulses and super-sensitive cameras, scientists found a quantum shortcut to compare two long lists of numbers, sending much less information than regular computers, especially for huge lists.

In depth

The paper experimentally demonstrates a quantum advantage in communication complexity for calculating the Euclidean distance between two real-valued vectors. This is achieved by using amplitude-modulated coherent states for encoding non-binary data, combined with superconducting nanowire single-photon detectors and a novel real-time visibility-gated acquisition technique. This approach allows for an exponential reduction in transmitted information compared to the best classical protocols, particularly for large input sizes up to

1 0^{8}

Key Takeaways

1
The study achieves an exponential quantum advantage in transmitted information for the Euclidean distance problem, surpassing the best classical protocol for input sizes up to $1 0^{8}$ .
2
The authors introduce amplitude-modulated encoding for non-binary, real-valued data, a significant advancement over previous binary quantum fingerprinting experiments.
3
The experimental setup leverages superconducting nanowire single-photon detectors and a real-time visibility-gated acquisition method to enable operation at extremely low photon numbers and mitigate phase fluctuations, crucial for practical implementation.

Conceptual Flow

HIGH LEVEL

Methodology: Quantum Euclidean Distance Protocol

Two friends send secret light signals to a referee, who then uses a special mirror and light sensors to figure out how different their secrets are, using very little information.

Friend A's Numbers

Friend B's Numbers

Send Light Signals

Referee's Light Sensors

Results: Exponential Communication Advantage

The new quantum way needs much less information to compare numbers than the best old ways, especially when the lists of numbers get really, really long.

Old Way: Lots of Data

New Way: Little Data

Compare Numbers

Faster, Cheaper Result