Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity

TL;DR

This paper experimentally demonstrates that using a quantum switch to create a superposition of communication directions enables an exponential reduction in communication complexity compared to classical and causally ordered quantum protocols.

Contribution

The authors realize a superposition of communication directions in a photonic system, experimentally confirming a quantum advantage in communication complexity using high-dimensional qudits.

Findings

Achieved less than 0.696 times the communication of causally ordered protocols.

Demonstrated exponential separation in communication complexity with high-dimensional quantum systems.

Opened new avenues for exploring indefinite causal structures experimentally.

Abstract

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.