Speaker
Description
A faithful reconstruction of a quantum many-body state enables the inference of physical properties not directly accessible from the input marginals. Achieving such predictive reconstruction is challenging because a tractable set of reduced density matrices does not generally determine the global state uniquely, and the many-body Hilbert space grows exponentially with system size. Here we develop a tensor-network tomography protocol that reconstructs a global matrix product state from a compact, physically designed set of reduced density matrices. Guided by the operator content of the critical theory, the selected subsystems combine nearest-neighbor spins, which probe local energy-like operators, with spatially separated spins, which constrain long-range spin correlations. The global state is optimized to minimize the quantum relative entropy between the input and reconstructed marginals for each selected subsystem. For critical Ising and three-state Potts chains up to around 64 sites, the protocol achieves global fidelities exceeding 99% and accurately reproduces universal long-distance correlation functions, substantially extending the accuracy and predictive scope demonstrated in earlier tensor-network tomography studies. Crucially, the reconstructed states recover nonlocal and universal properties not directly constrained by the tomographic input, including the universal scaling of the bipartite von Neumann entanglement entropy and the central charges, c=1/2 and c=4/5, of the two universality classes. Our results suggest a general design principle for efficient tomography of critical quantum states: select small marginals that simultaneously resolve the leading scaling dimensions via correlations.