Self-testing quantum state and apparatus in embedded system

Device-independent certification of quantum apparatus and quantum state has essential application in Quantum Communication and Quantum Computing. A stringent approach to certification is Quantum self-testing protocol, where minimum assumptions regarding the system and apparatus are taken into account; the only assumption is the compatibilities between observables. While there is significant progress in applying such kind protocol for the case of quantum communication, the literature for the case of quantum computing is limited. Our focus is the certifications of operators and states in different quantum computing systems, including topological qubits, cold atom, ion trap, etc., where qubits are not necessarily space-like separated. Regarding these kinds of systems, one can be skeptical and question the existence of entanglement between subsystems, or they want to characterize the measurement observables' fidelities. Quantum self-testing can help in this regard. We are adapting the protocols that are used in QKD and applying them to these cases. Currently, we are deriving the protocols which can calculate state and operator fidelities of these kinds of systems.