This study introduced distributed acoustic sensing (DAS) as an emerging sensing technique for large-scale traffic state perception (TSP) on expressways. By enabling optical fibers to operate as dense sensing arrays, DAS offered a promising solution for continuous traffic monitoring along expressway corridors. However, the raw traffic information extracted from DAS was inaccurate, which limited its direct application to large-scale TSP. This study proposed a physics-informed neural network (PINN) framework for DAS-based TSP. A physics-based DAS simulation platform was developed and validated against field observations, which provided a flexible testbed for generating data under diverse traffic scenarios. On this basis, two network architectures, residual U-Net (ResUNet) and Fourier neural operator (FNO), were investigated in combination with three types of traffic flow constraints, namely, the Lighthill-Whitham-Richards (LWR) model, LWR with a fundamental diagram (FD), and the Aw-Rascle-Zhang model. In total, 16 PINN models were constructed and evaluated. The results show that the proposed PINN framework effectively improves the accuracy of DAS-based TSP compared to the solely data-driven baselines. Among the physical constraints considered, the LWR-based models show the best overall performance. In addition, few-shot transfer learning can enhance model performance in previously unseen scenarios, demonstrating the potential of the proposed framework for adaptation to site-specific deployment conditions.