Comment on "A General Framework for Constructing Local Hidden-state Models to Determine the Steerability"

Based on the provided text, here is a detailed technical summary of the paper "Comment on 'A General Framework for Constructing Local Hidden-state Models to Determine the Steerability'" by Nick von Selzam and Florian Marquardt.

1. Problem Statement

The paper addresses a concern regarding academic attribution and originality in the field of quantum foundations. Specifically, the authors critique a recent preprint by Jia et al. (arXiv:2512.21848) which proposes a framework for constructing Local Hidden-State (LHS) models to determine quantum steerability.

Von Selzam and Marquardt argue that while Jia et al. cite their previous work (von Selzam & Marquardt, PRX Quantum, 2025), the citation fails to adequately reflect the extensive methodological overlap and significant textual similarity between the two papers. The core issue is that Jia et al. present a framework that closely mirrors the authors' earlier method for constructing Local Hidden-Variable (LHV) models, yet the presentation creates a false impression that the underlying framework is an original contribution of the Jia et al. paper.

2. Methodology of the Comment

The authors employ a comparative analysis to document the overlap between their 2025 PRX Quantum paper (Ref. [1]) and the 2025 arXiv preprint by Jia et al. (Ref. [2]). Their methodology involves:

• Concept Mapping: They identify specific technical components in Jia et al.'s paper (Sections III and IV) and map them directly to the corresponding sections in their own paper (Sections III, IV, and Appendix G.1).
• Textual Comparison: They perform a side-by-side analysis of specific passages, highlighting instances where Jia et al. have paraphrased or nearly reproduced text from the authors' work, often changing only variable names (e.g., $LHV \to LHS$, $k \to a$) or minor notation.
• Attribution Audit: They systematically check whether specific methodological elements in Jia et al.'s paper are explicitly attributed to the authors' prior work.

3. Key Contributions and Findings

The paper does not present new experimental data but rather a rigorous audit of scientific integrity and methodological derivation. The key findings are:

A. Methodological Overlap (Table I)

The authors demonstrate that nearly every core component of Jia et al.'s framework was previously established in their own work. Key overlapping concepts include:

• Representation: Using a finite cloud of hidden-variable tuples to represent distributions.
• Parametrization: Using Softmax functions to parametrize local measurement rules to ensure probability constraints.
• Basis Expansion: Expanding measurement operators into generalized Gell-Mann matrices (including a specific non-standard normalization for $G_0$) and expanding measurement rules into orthonormal basis functions.
• Optimization Strategy:
  • Defining hidden variables as coefficient matrices of the expansion.
  • Using odd spherical harmonics for projective qubit measurements.
  • Employing sigmoid functions to ensure non-vanishing gradients for numerical optimization.
  • Defining the loss function as the mean distance between the model and quantum statistics over all measurements.
  • Utilizing Stochastic Gradient Descent (SGD) with batch-sampled measurements (Monte Carlo estimation) to handle the continuum of measurements.

Finding: Out of the 10 major methodological elements listed, only one (the expansion into orthonormal basis functions) was explicitly cited by Jia et al. The other 9, including the core optimization and parametrization strategies, were not attributed.

B. Textual Similarity (Tables II & III)

The authors provide concrete examples of textual plagiarism or excessive paraphrasing.

• Loss Function Definition: The definition of the loss function, the interpretation of $L=0$, and the mathematical formulation of minimizing the distance between distributions are nearly identical, differing only in notation ($P_{QM}$ vs. $\sigma_{QM}$).
• Optimization Algorithm: The description of the iterative parameter update ($\theta_{new} = \theta_{old} - \eta \nabla_\theta L$) and the justification for using stochastic sampling (replacing the continuum mean with a Monte Carlo estimate) are structurally and linguistically almost identical.
• Specific Technical Details: Even niche details, such as the specific dimensionality formula for spherical harmonics ($d = \frac{1}{2}(D+1)(D+2)$) and the specific normalization choice for Gell-Mann matrices ($G_0 = \sqrt{2/d}I$), are reproduced with minimal variation.

C. The "New" Element

The authors acknowledge that Jia et al. did introduce one specific adaptation: the parametrization of hidden states via unconstrained complex matrices, which is specific to the steering problem (as opposed to the LHV problem). However, the authors argue that this specific adaptation does not justify the presentation of the entire framework as a novel contribution, especially given the lack of attribution for the underlying machine-learning-inspired architecture.

4. Results

The "result" of this paper is a formal documentation of the lack of appropriate attribution. The authors conclude that:

1. The framework presented by Jia et al. is a direct application of the authors' previously published LHV framework to the steering problem.
2. The presentation in Jia et al.'s paper conveys a false impression that the underlying framework is largely their own original contribution.
3. The extent of the overlap (both methodological and textual) is not adequately reflected by the limited citations provided in Jia et al.'s paper.

5. Significance

This comment is significant for several reasons:

• Scientific Integrity: It highlights the importance of distinguishing between a "reasonable extension" of a method and the presentation of that extension as a novel framework without acknowledging the foundational work.
• Methodological Clarity: It clarifies the lineage of machine-learning-inspired methods for constructing LHV/LHS models, ensuring credit is given to the original developers of the general framework (von Selzam & Marquardt).
• Community Standards: It serves as a case study for the quantum physics community regarding how to properly cite and build upon prior work, particularly when adapting methods from one domain (LHV) to another (Steering/LHS).

In summary, the paper asserts that while extending the framework to quantum steering is a valid scientific endeavor, the execution by Jia et al. fails to meet standards of attribution due to the unacknowledged reuse of both the core methodology and the specific phrasing of the original authors' work.