Can a classical system command a general adversarial quantum system torealize arbitrary quantum dynamics? If so, then we could realize the dream ofdevice-independent quantum cryptography: using untrusted quantum devices toestablish a shared random key, with security based on the correctness ofquantum mechanics. It would also allow for testing whether a claimed quantumcomputer is truly quantum. Here we report a technique by which a classicalsystem can certify the joint, entangled state of a bipartite quantum system, aswell as command the application of specific operators on each subsystem. Thisis accomplished by showing a strong converse to Tsirelson's optimality resultfor the Clauser-Horne-Shimony-Holt (CHSH) game: the only way to win many gamesis if the bipartite state is close to the tensor product of EPR states, and themeasurements are the optimal CHSH measurements on successive qubits. This leadsdirectly to a scheme for device-independent quantum key distribution. Controlover the state and operators can also be leveraged to create more elaborateprotocols for realizing general quantum circuits, and to establish that QMIP =MIP*.
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