Entanglement in prepare-and-measure scenarios: many questions, a few answers

TL;DR

This paper investigates how entanglement and quantum communication jointly influence correlations in prepare-and-measure scenarios, revealing that higher-dimensional entanglement enhances communication power and that certain low-capacity resources can produce stronger correlations.

Contribution

It characterizes entanglement-assisted prepare-and-measure scenarios with restricted entanglement, establishing relations between classical, quantum, and entanglement-assisted communication, and analyzing dense coding protocols.

Findings

Higher-dimensional entanglement enhances communication capacity.

Dense coding protocols can be understood as real-valued quantum protocols.

Small-capacity resources like qutrits can produce stronger correlations.

Abstract

Entanglement and quantum communication are paradigmatic resources in quantum information science leading to correlations between systems that have no classical analogue. Correlations due to entanglement when communication is absent have for long been studied in Bell scenarios. Correlations due to quantum communication when entanglement is absent have been studied extensively in prepare-and-measure scenarios in the last decade. Here, we set out to understand and investigate correlations in scenarios that involve both entanglement and communication, focusing on entanglement-assisted prepare-and-measure scenarios. In a recent companion paper [arXiv:2103.10748], we investigated correlations based on unrestricted entanglement. Here, our focus is on scenarios with restricted entanglement. We establish several elementary relations between standard classical and quantum communication and their entanglement-assisted counterparts. In particular, while it was already known that bits or qubits assisted by two-qubit entanglement between the sender and receiver constitute a stronger resource than bare bits or qubits, we show that higher-dimensional entanglement further enhance the power of bits or qubits. We also provide a characterisation of generalised dense coding protocols, a natural subset of entanglement-assisted quantum communication protocols, finding that they can be understood as standard quantum communication protocols in real-valued Hilbert space. Though such dense coding protocols can convey up to two bits of information, we provide evidence, perhaps counter-intuitively, that resources with a small information capacity, such as a bare qutrits, can sometimes produce stronger correlations. Along the way we leave several conjectures and conclude with a list of interesting open problems.