Almost device-independent calibration beyond Born’s rule: Bell tests for cross-talk detection

Abstract In quantum information, device-independent (DI) protocols offer a new approach to information processing tasks, making minimal assumptions about the devices used. Typically, since these protocols draw conclusions directly from the data collected in a meaningful Bell test, the no-signaling conditions, and often even Born’s rule for local measurements, are taken as premises of the protocol. Here, we demonstrate how to test such premises in an (almost) DI setting, i.e. directly from the raw data and with minimal assumptions. In particular, for IBM’s quantum computing cloud services, we implement the prediction-based ratio protocol to characterize how well the qubits can be accessed locally and independently. More precisely, by performing a variety of Clauser–Horne–Shimony–Holt-type experiments on these systems and carrying out rigorous hypothesis tests on the collected data, we provide compelling evidence showing that some of these qubits suffer from measurement cross-talks, i.e. their measurement statistics are affected by the choice of measurement bases on another qubit. Unlike standard randomized benchmarking, our approach does not rely on assumptions such as gate-independent Markovian noise. Moreover, despite the relatively small number of experimental trials, the direction of ‘signaling’ may also be identified in some cases. Our approach thus serves as a complementary tool for benchmarking the local addressability of quantum computing devices.