Finite-copy risk for polynomial energies of thermal Gaussian states
Scott Schubr, Luminary Oddities

main.pdf contains the manuscript. main.tex is its editable LaTeX source.

Build with Python 3 and Tectonic:
  python build.py --engine tectonic --output-dir build

Run the exact-arithmetic examples with Python 3 (standard library only):
  python verify_moments.py
  python verify_heterodyne.py

The verification program compares a normal-order operator expansion with
the reduced-tensor moment formula in seven signed two-mode cases, checks
six isotropic two-mode product-energy cases and their displayed table,
and verifies 64 scalar negative-binomial identities. It also checks the
two numerical copy-budget scales. These are finite exact-arithmetic checks;
the manuscript supplies the general analytic proofs and covariance convention.
The same program checks the displayed same-target pooling benchmark and
64 instances of the finite-copy product-polynomial resource bound.

verify_heterodyne.py separately expands the complex coherent polynomial,
applies the finite inverse heat operator, and evaluates exact Gaussian moments.
Eight anisotropic two-mode cases check the two-sided contraction formula.
Each contraction order also checks the pointwise quantum/heterodyne noise bounds.
The checks also distinguish it from a one-sided squared-noise substitution.

The paper includes pointwise minimum-variance unbiased optimality, the fixed-floor
growing-degree critical biased minimax limit, and a matched all-heterodyne risk
comparison. The quantum measurement is the spectral measurement of the averaged
collective observable. All source and code dependencies are contained here.

citation.json provides bibliographic metadata. MANIFEST.sha256 lists the
SHA-256 hashes of the other files in this source package.
