Direct Quantum Process Tomography for Arbitrary Qubit Systems Without Auxiliary States

Quantum process tomography is an effective method for measuring the quantum channel parameters in the field of quantum information. However, standard quantum process tomography (SQPT) cannot obtain arbitrarily specific process-matrix elements because it requires a global reconstruction algorithm. Direct quantum tomography can be used to obtain specific matrix elements of interest without the need for a global reconstruction algorithm. Therefore, direct process quantum tomography (DQPT) has attracted widespread attention. DQPT based on weak measurements has been recently proposed. However, additional auxiliary states and post-selection processes are necessary in these schemes, which increases the complexity of practical experiments and reduces the utilization of measurement resources. In this study, a DQPT protocol without the assistance of pointer states is proposed, which reduces the complexity of practical experiments. Subsequently, the scheme is generalized to arbitrary qubit systems and experimentally perform the protocol on a nuclear magnetic resonance (NMR) system provided by a quantum cloud platform. Finally, considering that when the qubit resources are insufficient, a superimposed coherent state is used as the pointer state to complete the direct characterization of a quantum process. The measurement protocol is easily scalable and integrated, laying the foundation for direct tomography on a chip.