Quantum Decision Theory for Displacement Detection with Finite-Energy GKP States

• URL: http://arxiv.org/abs/2608.08051v1
• Date: Sat, 08 Aug 2026 10:32:05 GMT
• Title: Quantum Decision Theory for Displacement Detection with Finite-Energy GKP States
• Abstract summary: We develop a framework for detecting phase-space displacements with finite-energy, $d$-level Gottesman-Kitaev-Preskill (GKP) probes.<n>For single-mode and entanglement-assisted architectures, we derive the Bayesian minimum-error probability.<n>We benchmark the resulting protocols against coherent-state, direction-matched squeezed-vacuum, and twin-beam schemes.
• Score: 46.2474896050764
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 characteristic, and the corresponding minimum detectable displacement. Finite-energy effects are treated through exact theta-series displacement kernels, while pure loss followed by quantum-limited amplification is mapped to an effective Gaussian random-displacement channel. Entanglement removes preparation-dependent blind directions and preserves both logical displacement labels, although it does not surpass the pointwise optimized single-mode strategy in the noiseless pure-state setting. We benchmark the resulting protocols against coherent-state, direction-matched squeezed-vacuum, and twin-beam schemes at equal nominal squeezing. Numerical results identify finite-squeezing and lossy regimes in which GKP probes achieve both a lower Bayesian error and a smaller minimum detectable perturbation than the selected Gaussian receivers.

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