Robust Self Testing of All Pure Bipartite Maximally Entangled States via Quantum Steering.

The idea of self-testing is to render guarantees concerning the inner workings of a device based on the measurement statistics. It is one of the most formidable quantum certification and benchmarking schemes. Here, we have shown that any bipartite pure entangled state can be self-tested through Quantum Steering. Analogous to the tilted CHSH inequality, we use a steering inequality called Tilted Steering Inequality for self-testing any pure two-qubit entangled state. We have further used this inequality to self-test any bipartite pure entangled state by certifying two-dimensional sub-spaces of the qudit state by observing the structure of the set of assemblages obtained on the trusted side after measurements are made on the un-trusted side. Finally, as a novel feature of self testing via steering, we use the notion of Assemblage based Robust Self Testing to provide robustness bounds for the self testing result in the case of pure maximally entangled states of any local dimension.