Abstract
Demonstrating a quantum advantage with currently available experimental systems is of utmost importance in quantum information science. While this remains elusive for quantum computation, the field of communication complexity offers the possibility to already explore and showcase this advantage for useful tasks. Here, we define such a task, the Sampling Matching problem, which is inspired by the Hidden Matching problem and features an exponential gap between quantum and classical protocols in the one-way communication model. Our problem allows by its conception a photonic implementation based on encoding in the phase of coherent states of light, the use of a fixed size linear optic circuit, and single-photon detection. This enables us to demonstrate in a proof-of-principle experiment an advantage in the transmitted information resource over the best known classical protocol, something impossible to reach for the original Hidden Matching problem. Our demonstration has implications in quantum verification and cryptographic settings.
Highlights
Demonstrating a quantum advantage with currently available experimental systems is of utmost importance in quantum information science
We apply the aforementioned coherent state mapping to Sampling Matching and we show that its implementation in this framework requires a single beam splitter and two detectors, contrary to the original Hidden Matching problem that would require the number of active components to increase at least logarithmically with the input size of the problem
We start by defining a one-way communication task that we call Sampling Matching (SM), which is inspired by the Hidden Matching (HM) problem defined in refs. 31,34
Summary
Demonstrating a quantum advantage with currently available experimental systems is of utmost importance in quantum information science. A significant step in the direction of experimental quantum communication complexity was made by theoretical work proposing a mapping for encoding quantum communication protocols involving pure states of many qubits, unitary operations, and projective measurements to protocols based on coherent states of light in a superposition of optical modes, linear optics operations, and single-photon detection[35]. This model was used to propose the practical implementation of coherent state quantum fingerprints for computing the equality function in the simultaneous message passing model of communication complexity[36], leading to experiments demonstrating a quantum advantage in the transmitted information in this model[37,38]
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