On the Duality of Teleportation and Dense Coding

Abstract

Quantum teleportation is a quantum communication primitive that allows a long-distance quantum channel to be built using pre-shared entanglement and one-way classical communication. However, the quality of the established channel crucially depends on the quality of the pre-shared entanglement. In this work, we revisit the problem of using noisy entanglement for the task of teleportation. We first show how this problem can be rephrased as a state discrimination problem. In this picture, a quantitative duality between teleportation and dense coding emerges in which every Alice-to-Bob teleportation protocol can be repurposed as a Bob-to-Alice dense coding protocol, and the quality of each protocol can be measured by the success probability in the same state discrimination problem. One of our main results provides a complete characterization of the states that offer no advantage in one-way teleportation protocols over classical states, thereby offering a new and intriguing perspective on the long-standing open problem of identifying such states. This also yields a new proof of the known fact that bound entangled states cannot exceed the classical teleportation threshold. Moreover, our established duality between teleportation and dense coding can be used to show that the exact same states are unable to provide a non-classical advantage for dense coding as well. We also discuss the duality from a communication capacity point of view, deriving upper and lower bounds on the accessible information of a dense coding protocol in terms of the fidelity of its associated teleportation protocol. A corollary of this discussion is a simple proof of the previously established fact that bound entangled states do not provide any advantage in dense coding. I. INTRODUCTIONQuantum teleportation [4] is one of the most important protocols in quantum information theory. It provides the backbone for a number of applications such as quantum communication [5], long-distance entanglement distribution via repeaters [7], and quantum computation [12]. From a fundamental perspective, teleportation beautifully demonstrates the interplay between different quantum resources: one communication primitive, a qubit channel, can be simulated using two other communication primitives, pre-shared entanglement and a two-bit classical channel. Consequently, universal distributed quantum computation can be achieved using preshared entanglement along with local operations and classical communication (LOCC). The rich study of entanglement and LOCC within quantum information science was largely due to this realization [19].

Asymptotic teleportation scheme bridging between standard and port-based teleportation

“…This paradigm-shifting protocol exploits the non-local properties of quantum entanglement, a phenomenon that Albert Einstein famously critiqued as 'spooky action at a distance.' Over the past three decades, quantum teleportation has not only been theoretically refined but also experimentally demonstrated [2][3][4] and developed [5][6][7], marking significant milestones in the fields of quantum computation and information [8][9][10][11]. Building upon these foundational achievements, quantum teleportation has accelerated the development of advanced quantum technologies, including entanglement swapping [12], quantum repeaters essential for long-distance quantum communication [13,14], quantum gate teleportation [15], quantum cryptography [16], and measurement-based computation [17].…”