Quantification of Quantum Dynamical Properties with Two Experimental Settings

Characterizing quantum dynamics is essential for quantifying arbitrary properties of a quantum process -- such as its ability to exhibit quantum-mechanical dynamics or generate entanglement. However, current methods require a number of experimental settings that increases with system size, leading to artifacts from experimental errors. Here, we propose an approximate optimization method that estimates property measures using only two mutually unbiased bases to compute their lower and upper bounds, and to reconstruct the corresponding processes. This system-size independence prevents error accumulation and allows characterization of the intrinsic quantum dynamics. Compared with quantum process tomography, we experimentally validate our method on photonic fusion and controlled-NOT operations, demonstrating accurate resource estimation while substantially reducing the number of required Pauli experimental settings: from 81 to 10 for the photonic fusion and to 2 for the controlled-NOT. These results show that our method is well-suited for estimation of dynamical properties in architectures ranging from chip-scale quantum processors to long-distance quantum networks.