Verification of quantum-gate teleportation based on Bell nonlocality in a black-box scenario

Quantum gate teleportation (QGT) is an excellent candidate for implementing remote quantum gate operations in large-scale quantum computer networks as it has the minimum resource demand to realize such computing models. The Bell nonlocality of quantum entanglement channel in QGT can be transformed into the corresponding posterior statistics correlation obtained by local measurements after QGT operation, and this Bell-type-like correlation can be used to check device and measurement loopholes or information leaking in the teleportation systems. In this paper, we propose a verification scheme based on Bell nonlocality for quantum CNOT gate teleportation in a black-box scenario where the vendors may not be trusted. The double criteria of high fidelity ((F) over bar > 97.53%) and high CHSH inequality violation (CHSH > 2) are used for assessing a vendor's reliability. The clients can use our scheme to check whether vendors employ classical simulation techniques to forge nonlocal quantum computing processes and it could provide a secure manner for the construction of quantum computer networks in the future.