Benchmarking quantum state transfer on quantum devices

Quantum state transfer (QST) provides a method to send arbitrary quantum states from one system to another. Such a concept is crucial for transmitting quantum information into the quantum memory, quantum processor, and quantum network. The standard benchmark of QST is the average fidelity between the prepared and received states. In this work we provide a new benchmark which reveals the nonclassicality of QST based on spatiotemporal steering (STS). More specifically, we show that the local-hidden-state (LHS) model in STS can be viewed as the classical strategy of state transfer. Therefore, we can quantify the nonclassicality of the QST process by measuring the spatiotemporal steerability. We then apply the spatiotemporal steerability measurement technique to benchmark quantum devices including the IBM quantum experience and QuTech quantum inspire under QST tasks. The experimental results show that the spatiotemporal steerability decreases as the circuit depth increases, and the reduction agrees with the noise model, which refers to the accumulation of errors during the QST process. Moreover, we provide a quantity to estimate the signaling effect which could result from gate errors or intrinsic non-Markovian effect of the devices.