Augmented-Lagrangian Determination of Pure-State Uniqueness in Quantum Tomography
A unified Augmented Lagrangian Method framework for deciding whether a pure quantum state is uniquely determined among pure states (UDP) or among all states (UDA) from a subset of measurements. A proved existence theorem for low-rank solutions recasts the convex UDA problem with low-rank constraints to cut variable count, while ALM handles the non-convex UDP optimization; experiments on qutrits and four-qubit symmetric states map states into the UDA / UDP-not-UDA / neither categories.
2501.00327
This quant-ph paper studies when a pure quantum state can be uniquely reconstructed from only a subset of measurements, rather than the O(d^2) measurements a general d-dimensional state needs. It wor…