Abstract We investigate prepare-and-measure scenarios in which a sender and a receiver use entanglement to send quantum information over a channel with limited capacity. We formalise this framework, identify its basic properties and provide numerical tools for optimising quantum protocols for generic communication tasks. The seminal protocol for sending quantum information over a classical channel is teleportation. We study a natural stochastic generalisation in which the sender holds N qubits from which the receiver can recover one on demand. We show that, if the classical communication is allowed to exploit extremal non-signalling correlations, then two bits of communication suffice to solve this task exactly for any N . We then consider entanglement-based protocols and show that these can be constructed systematically by leveraging connections to several well-known quantum information primitives, such as teleportation, cloning machines and random access coding. In particular, we show that by using genuine multi-particle entangled measurements, one can construct a universal stochastic teleportation machine, i.e. a device whose teleportation fidelity is independent of the quantum input.
Abstract We investigate prepare-and-measure scenarios in which a sender and a receiver use entanglement to send quantum information over a channel with limited capacity. We formalise this framework, identify its basic properties and provide numerical tools for optimising quantum protocols for generic communication tasks. The seminal protocol for sending quantum information over a classical channel is teleportation. We study a natural stochastic generalisation in which the sender holds N qubits from which the receiver can recover one on demand. We show that, if the classical communication is allowed to exploit extremal non-signalling correlations, then two bits of communication suffice to solve this task exactly for any N . We then consider entanglement-based protocols and show that these can be constructed systematically by leveraging connections to several well-known quantum information primitives, such as teleportation, cloning machines and random access coding. In particular, we show that by using genuine multi-particle entangled measurements, one can construct a universal stochastic teleportation machine, i.e. a device whose teleportation fidelity is independent of the quantum input.
Prepare-and-measure scenarios are among the simplest and most widely used settings for quantum communication. A sender prepares a physical system in one of several possible states, which a receiver then measures. Despite this simple structure, these scenarios offer a rich framework for exploring the differences between classical and quantum communication, revealing quantum advantages, and developing protocols for quantum cryptography and device certification. In this tutorial, we give a ground-up introduction to prepare-and-measure scenarios and the methods used to study them. We introduce different frameworks for constraining and characterising communication, with an emphasis on semi-device-independent approaches to quantum information. We also cover modern convex-optimisation techniques for characterising the correlations achievable in these scenarios and illustrate how these tools can be applied in practice. Our aim is to give newcomers the conceptual and technical foundations needed to approach the current literature and apply prepare-and-measure methods in their own research. We conclude with a discussion of open problems and directions for future work.
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 (PM) scenarios in the last decade. Here, we set out to understand and investigate correlations in scenarios that involve both entanglement and communication, focussing on entanglement-assisted (EA) PM 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 EA 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 EA 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.
Abstract Prepare-and-measure scenarios (pm), in their many forms, can be seen as the basic building blocks of communication tasks. As such, they can be used to analyze a diversity of classical and quantum protocols—of which dense coding and random access codes are key examples—in a unified manner. In particular, the use of entanglement as a resource in pm scenarios have only recently started to be systematically investigated, and many crucial questions remain open. In this work, we explore such scenarios and provide answers to some seminal questions. More specifically, we show that, in scenarios where entanglement is a free resource, quantum messages are equivalent to classical ones with twice the capacity. We also prove that, in such scenarios, it is always advantageous for the parties to share entangled states of dimension greater than the transmitted message. Finally, we show that unsteerable states cannot provide advantages in classical communication tasks, thus proving that not all entangled states are useful resources in these scenarios.
Quantum teleportation and Bell measurements are considered in a noisy relay setting. We introduce two quantum relay-channel models with closed-form capacity formulas, motivated by the canonical quantum communication protocols of teleportation and superdense coding. In both models, the sender transmits a qubit, while the relay observes side information about the Pauli errors that occur in the channel and communicates with the receiver through an orthogonal rate-limited link. We develop a compress-forward coding scheme in which the relay compresses the Pauli-error sequence into bins and sends the bin index to the receiver. The receiver uses this partial error information to reduce the effective channel noise before quantum decoding. We show that this strategy is optimal by establishing matching converse bounds for both models.
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.
Quantum entanglement plays a central role in many quantum communication protocols. It allows distant particles to share correlations beyond the limits of classical interactions. Entanglement is essential for superdense coding, quantum teleportation, and secure cryptographic key distribution in quantum communication. It is also a pillar for developing quantum networks, where the management and distribution of entanglement are crucial for connecting distant nodes. Although perfect entanglement is a sought-after ideal, experimental imperatives, including entanglement distribution over long distances, often limit the quality of entangled states. An important question is whether weaker entanglement still offers advantages. First, we study more general tasks than dense coding to show that simpler measurements, combined with entanglement, allow advantageous and sometimes even optimal qubit communication protocols to be obtained. We also demonstrate that simple measurements can generate quantum correlations that cannot be modelled by two classical communication bits and can constitute an optimal protocol with quantum resources. We implement a novel Bell-type inequality tailored for certifying full network non-locality (FNN) to develop certification methods guaranteeing security on an entanglement-based network. Our experiment uses two pairs of polarised entangled photons in a network configuration with three nodes, briefly referred to as a bilocal network scenario. Finally, we show that weakly entangled states can improve communication over a qubit channel using only separate (local) measurements on isotropic non-steerable two-qubit states, without interference, of individual photons, across two communication tasks: secret sharing and its stochastic variant.