Understand
Quantum state discrimination is a fundamental primitive in quantum information processing, underpinning tasks in quantum communication, sensing, and learning.
- We consider the general Bayes framework, as introduced by Helstrom, for state discrimination when, instead of a classical description of the candidate states, one has access to their \emph{source code}: the quantum circuit that prepares them.
- We show that the semidefinite program (SDP) for the discrimination problem can be reformulated in terms of the Gram matrix of these states, reducing the SDP variable dimensions from $dL$ to $NL$, where $d$ is the Hilbert space dimension, $N$ is the number of candidate states, and $L$ is the number of possible guesses.
- Importantly, we further introduce a quantum pre-processing procedure which efficiently constructs the reduced semidefinite program from the source code, enabling our method to operate directly on quantum data.