pith:BHIDWZHM
Singular Asymptotics of SPADE in Quantum Source Discrimination
SPADE and direct imaging share the same leading log canonical threshold but differ in multiplicity for aligned sources, while misalignment shifts their discrimination scales and creates an exact blind separation for binary-SPADE.
arxiv:2605.14432 v1 · 2026-05-14 · quant-ph · math.ST · stat.ME · stat.TH
Add to your LaTeX paper
\usepackage{pith}
\pithnumber{BHIDWZHMCCWWEZOGXS6YFL42XD}
Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge
Record completeness
Claims
In the aligned Gaussian case, direct imaging and SPADE share the same real log canonical threshold λ=1/2 but differ in multiplicity, yielding a universal subleading advantage of aligned SPADE in the local prior-weighted regime. In the misaligned setting, 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, with binary-SPADE exhibiting an exact blind separation s*=2θ.
The analysis assumes a Gaussian point-spread function and that a binary-SPADE reduction retains the full leading O(s^2) leakage contrast near alignment, with higher-mode corrections entering only at O(s^4); if the actual optical response deviates from this model, the claimed scaling and blind-spot results may not apply.
Aligned SPADE shares the log canonical threshold λ=1/2 with direct imaging but gains a subleading advantage, while misaligned binary-SPADE shows different power scaling and an exact blind spot at s*=2θ.
References
Receipt and verification
| First computed | 2026-05-17T23:39:07.118967Z |
|---|---|
| Builder | pith-number-builder-2026-05-17-v1 |
| Signature | Pith Ed25519
(pith-v1-2026-05) · public key |
| Schema | pith-number/v1.0 |
Canonical hash
09d03b64ec10ad6265c6bcbd82af9ab8ebea5143e522e11274db5561ddc80620
Aliases
· · · · ·Agent API
Verify this Pith Number yourself
curl -sH 'Accept: application/ld+json' https://pith.science/pith/BHIDWZHMCCWWEZOGXS6YFL42XD \
| jq -c '.canonical_record' \
| python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 09d03b64ec10ad6265c6bcbd82af9ab8ebea5143e522e11274db5561ddc80620
Canonical record JSON
{
"metadata": {
"abstract_canon_sha256": "3f7931c5bfa534c003107168d5f03d66ce490023d0399f9ff3bb3b58ef306aa3",
"cross_cats_sorted": [
"math.ST",
"stat.ME",
"stat.TH"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"primary_cat": "quant-ph",
"submitted_at": "2026-05-14T06:26:41Z",
"title_canon_sha256": "81910edc13e39faa1b1a2ba7ff5c5437f9adf0c4b1afd0260904b4b4b0bea922"
},
"schema_version": "1.0",
"source": {
"id": "2605.14432",
"kind": "arxiv",
"version": 1
}
}