Quantum Decision Theory for Displacement Detection with Finite-Energy GKP States
We develop a quantum-decision-theoretic framework for detecting phase-space displacements with finite-energy, $d$-level Gottesman-Kitaev-Preskill (GKP) probes. For single-mode and entanglement-assisted architectures, we derive the Bayesian minimum-error probability, the optimal Neyman-Pearson receiver-operating charact...