Sarvagya Upadhyay

Quantum state discrimination is a fundamental primitive in quantum information processing, underpinning tasks in quantum communication, sensing, and learning. We study this problem through the lens of semidefinite programming and develop a general dimension-reduction framework for optimal discrimination. Our approach applies to (i) ensembles of pure states (not necessarily linearly independent), (ii) mixed states, and (iii) fully general discrimination settings in which the set of guesses and the reward assigned to each guess--state pair are arbitrary. This formulation encompasses standard minimum-error discrimination, minimum-error exclusion, discrimination with penalties for incorrect guesses, and structured reward models arising in problems such as quantum anomaly detection. We show that the resulting semidefinite program can be reduced from dimension $dL$ to $NL$, where $d$ is the Hilbert space dimension of the states, $N$ is the number of candidate states, and $L$ is the size of the set of possible guesses. Importantly, we further introduce a quantum pre-processing procedure which, given quantum access to the states to be discriminated, efficiently constructs the reduced semidefinite program, enabling our method to operate directly on quantum data. As an application, we characterize optimal identification probabilities for quantum changepoint problems in several regimes, including multiple-changepoint settings that were previously computationally inaccessible.