Device-independent verification of controlled non-local CNOT quantum gate

Controlled non-local quantum gate operations reveal the cooperative and supervisory relationships of the controller and the non-local gate operators in a quantum networks, which is an essential feature for building multi-party quantum computing networks, and their security relies on quantum entanglement resources. To understand the behavior of vendors who substitute quantum entanglement resources with classical-quantum hybrid resources, this paper proposes a device-independent verification scheme for controlled non-local CNOT quantum gates. Moreover, it formulates a Svetlichny-type inequality to conduct an effective verification of the utilization of entanglement resources in nonlocal gate operations, particularly in instances where the Svetlichny inequality is not applicable. Our scheme offers a theoretical foundation for constructing secure distributed quantum computing networks in the future.