Entanglement has the ability to enhance the transmission of classical information over a quantum channel. However, fully harvesting this advantage typically requires complex entangling measurements, which are challenging to implement and scale with the system’s size. In this Letter, we consider a natural quantum information primitive known as a random access code in which the message to be communicated is selected stochastically. We introduce a protocol that leverages high-dimensional entanglement to perform this task perfectly, without requiring quantum interference between particles at the measurement station. We experimentally demonstrate how this unlocks implementation in the high-dimensional regime through an optical setup using eight-dimensional entanglement and multioutcome detection, providing a practical solution for stochastic communication and a robust method for certifying the dimensionality of entanglement in communication experiments.

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• Quantum channels
• Quantum communication, protocols & technology
• Quantum entanglement
• Quantum information processing