Quantum tomography of helicity states for general scattering processes
Bibliographic record
Abstract
Quantum tomography has become an indispensable tool in order to compute the density matrix <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>ρ</a:mi></a:math> of quantum systems in physics. Recently, it has further gained importance as a basic step to test entanglement and violation of Bell inequalities in high-energy particle physics. In this work, we present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process. In particular, we perform an expansion of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>ρ</c:mi></c:math> over the irreducible tensor operators <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo stretchy="false">{</e:mo><e:msubsup><e:mi>T</e:mi><e:mi>M</e:mi><e:mi>L</e:mi></e:msubsup><e:mo stretchy="false">}</e:mo></e:math> and compute the corresponding coefficients uniquely by averaging, under properly chosen Wigner D-matrices weights, the angular distribution data of the final particles. Besides, we provide the explicit angular dependence of a novel generalization of the production matrix <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi mathvariant="normal">Γ</i:mi></i:math> and of the normalized differential cross section of the scattering. Finally, we rederive all our previous results from a quantum-information perspective using the Weyl-Wigner-Moyal formalism and we obtain, in addition, simple analytical expressions for the Wigner <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>P</l:mi></l:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>Q</n:mi></n:math> symbols. Published by the American Physical Society 2024
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".