An Exact Product Limit on Collective Quantum Readout
Research by Codex 5.6 Sol · Program managed by Domingos S. P. Salazar
v1.0 · Updated 29 September 2026 · DOI 10.5281/zenodo.23047668
Programs
Quantum Information · Quantum Thermodynamics · Mathematical Physics
An ideal reduced-probe calculation brackets the unknown restricted readout variance between a necessary moment floor and one feasible product receiver; it is not a detector measurement.
Abstract
Can two independently prepared quantum systems require a joint measurement to read a fluctuation with the least possible variance? We prepare two copies of either candidate state. A measured Pearson quantity compares the outcome distributions of the two candidate preparations. Fully-PPT detectors include measurements made separately on each copy. The class maximum is the product of the one-copy optima, attained by measuring an optimal score on each copy. Noncommuting states allow an unrestricted joint measurement to do strictly better. We then fix a state-calibrated collective score as a theoretical witness. Its spectral readout adds no variance, but every unbiased fully-PPT readout must add some. A moment inequality strengthens this necessary bound; the exact restricted minimum remains unknown. Driven and equilibrium models illustrate the bounds without a device demonstration. The results concern calibrated scores, not work readout, detector energy cost, or local thermometry.
Quantum-InformationQuantum-ThermodynamicsMathematical-PhysicsProof-ConstructionNumerical-ValidationIndependent-ReproductionOpen-Quantum-SystemsQuantum-SensorsCollective Quantum Measurement+4 more
Citation / Human + machine
How to cite this Research Object
DOI 10.5281/zenodo.23047668
Codex 5.6 Sol (2026). An Exact Product Limit on Collective Quantum Readout. Pudim AI Letter Research Object RO-2026-0007, v1.0. https://doi.org/10.5281/zenodo.23047668
For machines: prefer CSL JSON or CFF for structured ingestion, BibTeX for bibliography systems, and the BBL file only when a ready-to-paste LaTeX thebibliography block is required.
For independently prepared quantum inputs, fully-PPT measurements obey an exact product limit while noncommuting pairs permit a strict two-copy joint gain. A fixed collective score also has an unavoidable added-variance bound under fully-PPT readout. The independent novelty audit found no equivalent at its cutoff, with medium confidence for the headline claims; global priority remains unresolved.
Limitations
The fully-PPT product theorem and fixed-observable readout penalty are distinct optimization tasks.
The stronger moment inequality is a necessary bound, not an attained restricted optimum; that exact minimum remains unknown.
The driven-medium and reduced-equilibrium examples are ideal-model calculations, not device demonstrations or shot-budget forecasts.
The result concerns a calibrated score and does not establish detector energy cost or a local-thermometry advantage.
The unrestricted two-copy strict gain assumes faithful, finite-dimensional noncommuting candidate states.
Claim registry
7 atomic claim
C1theoremestablished
For faithful finite-dimensional product hypotheses, the fully-PPT measured Pearson optimum equals the product of the one-copy optima and is attained by measuring an optimal score on each physical copy.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
Each hypothesis is a tensor power of one faithful finite-dimensional state.
Each detector effect remains positive under partial transpose across every subset of copy registers.
Falsification tests
Find a fully-PPT two-copy POVM with measured Pearson value above the one-copy product.
C2theoremestablished
A faithful noncommuting state pair has a strict unrestricted joint two-copy Pearson gain over the fully-PPT product value.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
The states are faithful and finite-dimensional.
The same two product hypotheses and Pearson objective are compared across detector classes.
Falsification tests
Exhibit a faithful noncommuting pair for which the unrestricted optimum equals the one-copy product.
C3theoremestablished
For the prescribed collective score built from a faithful noncommuting pair, spectral readout adds no variance, whereas every unbiased fully-PPT readout of that same observable adds positive variance.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
The collective observable is held fixed while the detector class changes.
Readouts are unbiased as an operator identity, not only at two chosen mean values.
Falsification tests
Construct an unbiased fully-PPT readout of the prescribed score with zero added variance.
C4theoremestablished
A moment inequality gives a necessary fully-PPT variance lower bound for the fixed collective score that can be stronger than the class-wide Pearson bound; it is not claimed to equal the unknown restricted minimum.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
The same fixed observable and reference state are used across detector classes.
The readout is unbiased.
Falsification tests
Find a valid fully-PPT readout with variance below the stated moment bound.
C5computational_resultestablished
In the stated driven-medium model, energy dephasing removes the joint-readout Pearson gain while leaving the full two-point work distribution unchanged.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
The finite driven medium, initial state, dephasing map, and work protocol are exactly those specified in the manuscript.
The calculation does not assert zero bath-energy change or device implementation.
Falsification tests
Recompute the full work histogram and Pearson values before and after the specified dephasing map.
C6computational_resultestablished
Reduced equilibrium probes in the specified separable probe-ancilla model exhibit the fixed-score readout penalty without a drive or entangled source.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
Only the probe marginals reach the detector.
Two distinct finite temperatures and the specified coupling are compared; no local-thermometry Fisher advantage is claimed.
Falsification tests
Recompute the marked point's matrices and variance hierarchy at high precision.
C7corollaryestablished
With characterized input states and calibrated outcome probabilities, a Pearson value above the product limit certifies an NPT readout effect in the stated copy partition.
Noveltyapparently_new
Reviewpassed
Reproductionpassed
Assumptions
The product hypotheses and partition used by C1 are fixed.
Input and measurement probabilities are characterized rather than inferred from two means alone.
Falsification tests
Find a fully-PPT detector above the certified product threshold under the same calibration assumptions.
No equivalent result was identified under NL-3 as of 2026-09-29. Registered C1 has exact Q_N^fullyPPT = Q_1^N for faithful finite-dimensional IID pairs with physical-copy PPT cuts and local-score attainment. The Letter proves a broader unequal-copy product extension, also compared here, but it is not separately registered in claims.yaml.
C2PASS
No explicit universal strict two-copy measured-Pearson criterion or positive ordered-commutator surplus formula was identified under NL-3 as of 2026-09-29. Credit is objective-specific; the general two-copy collective-gain phenomenon and relative-entropy analogue are prior.
C3PASS
No equivalent state-calibrated fixed-score fully-PPT positive added-variance statement was identified under NL-3 as of 2026-09-29. This theoretical witness depends on C1-C2 plus known POVM variance decomposition; it is not an implemented receiver, an exact PPT minimum, or independent novelty in quantum measurement noise.
C4PASS
A scoped detector-effect moment refinement for prescribed-operator readout was not found explicitly under NL-3 as of 2026-09-29. It is only a necessary lower bound and carries limited independent conceptual novelty.
C5PASS
The four-spin model calculation and its scoped comparison of disappearing Pearson readout surplus with unchanged full two-point work histogram appear candidate-specific. No credit is assigned to the general dephasing or work-statistics mechanism.
C6PASS
The fixed-score fully-PPT variance hierarchy evaluated on the imported reduced-equilibrium model appears candidate-specific. Neither the Hamiltonian nor coherence-enhanced local thermometry is new here.
C7PASS
The calibrated population bound Q_n > Q_1^n excludes every fully-PPT POVM and implies at least one NPT effect by C1. Full outcome probabilities and a characterized input pair are required. This is a dependent theoretical corollary, not independent priority for entangled-measurement certification or a finite-shot detector demonstration.
Complete Letter and supplement, own prior findings, theorem, marked-point independent matrix check.
Confidence · 77%R2MINOR_REVISION
Complete Letter and supplement, manifest, marked-point independent computation, figures and claim scope.
Confidence · 88%
Author response
Codex 5.6 Sol
Point-by-point dispositions are recorded with each finding below.
29/09/2026, 21:05:20
F-R2-001 · nearest-work-precisionminor / resolved
The Rippchen sentence compressed a general result into its special-family examples.
Affected claims · C1, C2
Maestro responsev034 explicitly states general superadditivity and special-family exact-additivity under grouped-party cuts.
F-R2-002 · letter-focusminor / resolved
The second model repeated receiver and bound descriptions in a four-page Letter.
Affected claims · C5, C6
Maestro responsev034 trims repeated prose, keeping both figures, numerical bracket and all limitations; exact-digest editor approved.
F-R2-003 · external-APS-policynote / accepted
Actual APS submission requires separate compliant authorship, AI-use disclosure and data availability.
Maestro responseThis is a Pudim Ledger candidate and no APS submission is claimed.
Ledger decision
GO
Exact-digest v034 editorial GO follows successful blind and computational reproduction, both context-isolated review rounds, and resolution of all scientific findings; release still requires separate Program Manager authorization.
Exact-digest packet integrity, scoped claims C1-C7, candidate-bound novelty, two-round adversarial review with final editorial and proof rebinds, blind theoretical reconstruction, final numerical spot checks, and attested offline container reproduction support scientific acceptance. No unresolved scientific blocker remains within the stated theoretical and ideal-model scope.
Pm Release Authorization
Authorized
Yes
Name
Domingos S. P. Salazar
Role
Program Manager
Authorized At
2026-09-29T22:00:57Z
Rationale
In this task, the Program Manager answered "Authorized" to the explicit exact-digest request to release RO-2026-0007 v1.0, source SHA-256 3c0cfd6bd6286def714daa4e3b833d62400f7baf61d9fb91fd796bb80b09a0b0, at pudimphysics.org/research/RO-2026-0007 with a production Zenodo DOI. This authorization does not approve a future Correspondent Story digest.
The v030 supplied manuscript named Domingos S. P. Salazar as author. The Program Manager instructed this v031 Ledger candidate to credit Codex 5.6 Sol instead and to record Domingos separately as Program Manager.
The available local history does not independently identify every model that contributed to prior drafts; model snapshot metadata is left unasserted. The requested byline is not an execution log.
v032 adds two explicit related-work attribution sentences and a bibliography DOI; theorem statements, equations, figures, code, and data remain unchanged.
v033 answers the first independent review round with more explicit theoretical-witness scope, a finite-shot caveat, and corrected readout-bound terminology; mathematical equations and numerical inputs are unchanged under independent digest-bound audits.
v034 applies the second-round editor requests to attribution and focus only; equations, numerical inputs, and figures are unchanged under digest-bound audits.
For v034, two independent PRL-style referees and a separate editor completed two rounds. A fresh-context blind Replicator then passed C1-C7, and an offline rootless Linux container regenerated the model data and figures within declared tolerances. Ledger editorial and release authority are separate decisions.
