Singular Asymptotics of SPADE in Quantum Source Discrimination

• URL: http://arxiv.org/abs/2605.14432v1
• Date: Thu, 14 May 2026 06:26:41 GMT
• Title: Singular Asymptotics of SPADE in Quantum Source Discrimination
• Abstract summary: We study far-field discrimination between one and two incoherent point sources in the singular regime of weak and closely spaced emitters.<n>Under ideal alignment, spatial-mode demultiplexing (SPADE) attains the quantum-trivial large-sample Stein singularity.<n>We show that misaligned binary-SPADE and direct imaging acquire non local power on different intrinsic scales.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study far-field discrimination between one and two incoherent point sources in the singular regime of weak and closely spaced emitters. Under ideal alignment, spatial-mode demultiplexing (SPADE) attains the quantum-optimal large-sample Stein exponent, but the finite-photon behavior near the one-source boundary and the effect of realistic imperfections remain less understood. Using singular learning theory, we analyze both the aligned and misaligned problems. In the aligned Gaussian case, we derive the zeta-function poles for direct imaging and SPADE, show that both share the same real log canonical threshold $λ=1/2$ but differ in multiplicity, and obtain the corresponding Bayes free-energy asymptotics. This yields a universal subleading advantage of aligned SPADE in the local prior-weighted regime. In the misaligned setting, we study a physically motivated binary-SPADE reduction that retains the full leading $O(s^2)$ leakage contrast near alignment, with corrections from the detailed higher-mode redistribution entering only at $O(s^4)$. We show that misaligned binary-SPADE and direct imaging acquire nontrivial local power on different intrinsic scales, $s=O(n^{-1/4})$ and $s=O(n^{-1/2})$, respectively. However, finite-$n$ Neyman--Pearson comparisons under common physical conditions reveal that direct imaging is stronger on the plotted grids and that misaligned binary-SPADE exhibits an exact blind separation $s^\ast=2θ$, where its power collapses to $α$. These results identify model singularity as a structural organizing principle for finite-photon quantum discrimination and clarify how ideal aligned SPADE benchmarks can fail to translate into finite-$n$ advantages under misalignment.

Related papers

• A variational physics-informed graph neural network for heterogeneous solid mechanics [0.0]
  This work presents a variational, label-free physics-informed graph neural network (PI-GNN) in which the conforming is carried by the discretization rather than by the trial field.
  arXiv  Detail & Related papers  (2026-09-10T02:02:32Z)
• Exact Quasiprobability Hierarchy of the Double-Morse Oscillator: From Potential Geometry to Operator Ordering [0.0]
  We develop an exact, representation-consistent analysis of the lowest quasi-exact ground state of the symmetric double-Morse oscillator.<n>In the double-Morse potential, the dimensionless parameter $A$ controls the separation of the minima and the central barrier.<n>We show that $A$ controls how the same non-Gaussian and nonclassical state is resolved across complementary representations.
  arXiv  Detail & Related papers  (2026-08-24T14:33:31Z)
• Near-Optimal Mode Scaling for Finite-Dimensional Boson Sampling via Lie-Algebraic Leakage Bounds [0.8594140167290097]
  Boson sampling on matter-based platforms requires encoding the bosonic modes in finite-dimensional local Hilbert spaces.<n>We develop a unified framework for non-interacting sampling on the irreducible representations of compact Lie groups.<n>We prove, in a Gaussian model of the transition matrix, that its spectral norm concentrates at $tildeO(stn)$ rather than the $O(n)$ worst-case of prior spin-based emulations.
  arXiv  Detail & Related papers  (2026-07-13T15:36:29Z)
• How Neural Reward Models Learn Features for Policy Optimization: A Single-Index Analysis [53.063298916923976]
  We study the feedback in a Gaussian single-index model with $r*(x) = *(langle *, xrangle)$ and $x sim N(0, I_d)$.<n>We analyze a two-stage neural reward model that first learns the hidden direction $*$ from reward-weighted samples and then fits the readout layer by weighted ridge regression.
  arXiv  Detail & Related papers  (2026-05-23T22:00:38Z)
• Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability [0.0]
  We identify the wavelet scaling exponent $$ as a critical diagnostic.<n>We establish $= 1/2$ as a sharp transition boundary for the classical simulability of amplitude-encoded quantum kernels.<n>We prove this variance scales strictly as $Var[X] = (d-2)$.
  arXiv  Detail & Related papers  (2026-05-12T05:41:12Z)
• The Spectral Edge Thesis: A Mathematical Framework for Intra-Signal Phase Transitions in Neural Network Training [0.0]
  We show that phase transitions in neural network training are controlled by the spectral gap of the rolling-window Gram matrix of parameter updates.<n>Adiabatic parameter $mathcalA = |G|_F / (, g2)$ controls circuit stability: $mathcalA ll 1$ (plateau), $mathcalA sim 1$ (phase transition), $mathcalA gg 1$ (forgetting)
  arXiv  Detail & Related papers  (2026-03-30T20:10:22Z)
• Regularized Online RLHF with Generalized Bilinear Preferences [68.44113000390544]
  We consider the problem of contextual online RLHF with general preferences.<n>We adopt the Generalized Bilinear Preference Model to capture preferences via low-rank, skew-symmetric matrices.<n>We prove that the dual gap of the greedy policy is bounded by the square of the estimation error.
  arXiv  Detail & Related papers  (2026-02-26T15:27:53Z)
• Unsupervised Discovery of Intermediate Phase Order in the Frustrated $J_1$-$J_2$ Heisenberg Model via Prometheus Framework [0.0]
  We apply the Prometheus variational autoencoder framework to explore the $J_1$-$J$ phase diagram.<n>We identify the structure factor $S(,)$ and $S(,)$ as the dominant order parameters.<n>This work establishes a scalable pathway for applying machine learning to frustrated quantum systems.
  arXiv  Detail & Related papers  (2026-02-25T00:44:51Z)
• Unregularized Linear Convergence in Zero-Sum Game from Preference Feedback [50.89125374999765]
  We provide the first convergence guarantee for Optimistic Multiplicative Weights Update ($mathtOMWU$) in NLHF.<n>Our analysis identifies a novel marginal convergence behavior, where the probability of rarely played actions grows exponentially from exponentially small values.
  arXiv  Detail & Related papers  (2025-12-31T12:08:29Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Programmable order by disorder effect and underlying phases through dipolar quantum simulators [0.0874967598360817]
  We study two different quantum simulators composed of molecules with dipole-dipole interaction. First result provides knowledge upon the quantum order by disorder effect of the $S=1/2$ system. Next, we study the dipolar bosonic model with tilted polar angle which can be realized through a quantum simulator.
  arXiv  Detail & Related papers  (2023-10-02T02:04:58Z)
• Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness [151.67113334248464]
  We show that extending the smoothing technique to defend against other attack models can be challenging. We present experimental results on CIFAR to validate our theory.
  arXiv  Detail & Related papers  (2020-02-08T22:02:14Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.