Quantum State Tomography

Quantum state tomography estimates a system’s density matrix—or properties such as fidelity—from measurements on repeated preparations, supporting the characterization and validation of quantum devices. Methods range from adaptive measurements and low-rank recovery to tensor-network models for structured many-body states and Bayesian or neural estimators that guide sampling or handle noise. Theory studies how the number of copies depends on dimension, rank, energy, and measurement capabilities, with bosonic Gaussian states and restricted joint measurements serving as important settings. A central challenge is balancing provable sample efficiency and reliable uncertainty estimates against computational cost and model bias, especially when learned reconstructions may rely more on prior structure than on measurement data.