Pith Number

pith:4I7GMOHO

pith:2026:4I7GMOHOG7F4HL2EOUJSB3X6BG

not attested not anchored not stored refs resolved

Closed-form Bayesian quantum estimation of Gaussian states

Edward Gandar, Jes\'us Rubio

A restriction to polynomial operators in quadratures reduces Bayesian quantum estimation of Gaussian states to closed-form linear problems.

arxiv:2605.16978 v1 · 2026-05-16 · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4I7GMOHOG7F4HL2EOUJSB3X6BG}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We introduce a variational framework reducing the optimisation over measurements and estimators to a finite-dimensional linear problem and admitting closed-form solutions. This is achieved by restricting the analysis to operators polynomial in the canonical quadratures, leading to solutions with a geometric interpretation as orthogonal projections of the global optimum.

C2weakest assumption

Restricting the measurement and estimator search to operators that are polynomials in the canonical quadratures is sufficient to produce solutions that are either optimal or near-optimal for the original unbounded problem.

C3one line summary

A variational framework yields closed-form Bayesian estimators for Gaussian quantum states via polynomial quadrature operators and a global optimality condition.

References

106 extracted · 106 resolved · 4 Pith anchors

[1] Closed-form Bayesian quantum estimation of Gaussian states 2026 · arXiv:2605.16978

[2] (24) can also be proven using the explicitly variational approach of Personick [19, 20], as shown in Appendix A

[3] This condition is sufficient wheneverSbelongs to the chosen polynomial subspaceV

[4] As shown in Appendix C, the MSL associated with an arbitrary Hermitian operatorXcan always be written as L(X) =L(S) +∥X− S∥ 2 ρ0 ,(35) whereL(X)is defined as in Eq

[5] Improved estimator based on posterior mean So far we have performed a constrained optimisation of the MSL by restricting the operatorM 1 to an operator subspace V. This optimisation jointly determines

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Closed-form Bayesian quantum estimation of Gaussian states

Receipt and verification

First computed	2026-05-20T00:03:34.149414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e23e6638ee37cbc3af44751320eefe09a59f40f72ba6dbdb4c306c3732f59d0c

Aliases

arxiv: 2605.16978 · arxiv_version: 2605.16978v1 · doi: 10.48550/arxiv.2605.16978 · pith_short_12: 4I7GMOHOG7F4 · pith_short_16: 4I7GMOHOG7F4HL2E · pith_short_8: 4I7GMOHO

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4I7GMOHOG7F4HL2EOUJSB3X6BG \
  | 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: e23e6638ee37cbc3af44751320eefe09a59f40f72ba6dbdb4c306c3732f59d0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e493d35b13c4a7ea7ffb893a23645a1713352d354e7777418a37c05dc5c02ae1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-16T12:56:59Z",
    "title_canon_sha256": "d0675d9330197971050bf9459ca23ab11387a1e05fb0c13ec951a182865bcab2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16978",
    "kind": "arxiv",
    "version": 1
  }
}