Semi-device-independent certification of entanglement in superdense coding

TL;DR

This paper presents a semi-device-independent method to certify entanglement in superdense coding, improving testing efficiency and enabling self-testing of maximally entangled states through a semidefinite programming approach.

Contribution

It reformulates superdense coding as a prepare and measure scenario, providing a novel entanglement witness and a method for self-testing and optimization using semidefinite programming.

Findings

Enhanced semi-device-independent entanglement certification

Method for self-testing maximally entangled states

Semidefinite program for optimizing superdense coding success

Abstract

Superdense coding is a paradigmatic protocol in quantum information science, employing a quantum communication channel to send classical information more efficiently. As we show here, it can be understood as a particular case of a prepare and measure experiment, a scenario that has attracted growing attention for its fundamental and practical applications. Formulating superdense coding as a prepare and measure scenario allows us to provide a semi-device-independent witness of entanglement that significantly improves over previous tests. Furthermore, we also show how to adapt our results into self-testing of maximally entangled states and also provide a semidefinite program formulation allowing to efficiently optimize, for any shared quantum state, the probability of success in the superdense coding protocol.