Device-Independent Framework for Self-testing Quantum states and measurements

Abstract

Quantum Key Distribution protocols are proven secure in theory, as their security relies on the concepts of quantum mechanics. It includes the disturbance created by the measurement and the No-cloning theorem. But in real experiments, there may be some imperfections in the devices (detectors or the photon source) which deviates them from the ideal behavior. To deal with this, we move to the scenario where we treated the devices as black boxes. Self-testing is a method which is independent of any specific device and can identify the properties of a physical device without knowing its internal structure or the Hilbert space dimension. Here we present a detailed proof of the self-testing method of entangled two-qubit state and three qubit W state in device-independent scenario. In self-testing, we only observe the probabilities p(a1a2|x1x2). Violation of the Bell inequalities allows to keep the correlations outside of the local polytope, ensuring that the correlations are produced by some quantum state.