Direct characterization of general quantum processes via generalized weak values.

Quantum dynamics governs the time evolution of quantum systems. Accurately characterizing these dynamical processes is crucial for deepening our understanding of fundamental physics and advancing quantum technologies. Quantum process tomography (QPT), the standard approach for characterization, reconstructs the representative matrix by preparing informationally complete sets of input states and measuring the output states. However, the experimental and algorithmic complexity of QPT increases dramatically with the size of the quantum system, significantly limiting its applicability to large-scale systems. Weak measurements on pre- and post-selected quantum systems yield generalized outcomes known as weak values. By establishing a direct relationship between weak values and the representative matrix elements, extracting these complex weak values enables the direct characterization of quantum systems. In recent years, this direct scheme has been successfully applied to various quantum states, single-qubit quantum processes, and quantum measurements. However, a universal direct scheme for the characterization of general quantum processes remains unexplored. Here, we propose a generalized weak value form that encompasses quantum processes, enabling the direct characterization of general quantum processes. Experimentally, we demonstrate the feasibility of our scheme by directly characterizing high-dimensional unitary processes, parity-time symmetric processes, two-qubit unitary processes, as well as single-qubit dephasing and amplitude damping processes, and two-qubit general quantum processes in a photonic platform. By generalizing the definition of weak value, our work not only expands the scope of weak measurements but also provides a promising approach for the characterization and exploration of large-scale quantum systems.