Research in the field of quantum physics is important for progress in many areas of exploration and development. Quantum computers and other quantum devices are promising technologies with numerous potential applications. On the other hand, understanding, interpreting, teaching, and learning quantum physics as part of an educational process is a major challenge. In the Republic of Croatia, students usually come in contact with the concepts of quantum physics towards the end of their high school education. These concepts are often abstract and represent a remarkable leap from the theories of classical physics. The aim of this study is to test the measurement properties of the instrument used to assess the progress of understanding and knowledge of quantum physics in a sample of Croatian high school students. The quantum physics conceptual survey (QPCS), developed and first tested in 2006 by Wuttiprom et al. at the University of Sydney, was the instrument we used in this study. The test was administered to 76 high school students. The results show that the QPCS test is valid and generally reliable in the context of Croatian secondary education, but for the topics Waves and particles and Uncertainty principle, the reliability needs further investigation. The results of the pretest and posttest were analysed and compared with each other and with previously published results. Quantitative methods were used to analyse the results obtained. We present several possible solutions to improve the teaching process, that we expect will lead to better results, especially for topics that are challenging for students.

We present a quantum-inspired model that embeds biomedical observables as state vectors in a Hilbert space and applies the spectral theory of Hermitian operators to identify a system's natural degrees of freedom as the eigenmodes of a constructed operator, en-abling the analysis of high-dimensional, multifactorial, strongly correlated biomedical systems whose dependency structures are often not captured by linear reductionist ap-proaches. Pairwise dependencies are encoded via off-diagonal elements representing generalised mutual information, estimated from joint and marginal Shannon entropies without parametric assumptions. Diagonalisation yields eigenvalues that quantify in-dependent biomedical drivers and eigenvectors that identify their collective modes. We validate the model on a breast cancer gene expression benchmark spanning three breast cancer subtypes and normal tissue, resolving five data-driven eigenmodes, two more than linear PCA, while three kernel PCA variants independently confirm the same subtype ordering as intrinsic to the data manifold. Beyond this benchmark, we develop a comparative framework specifying what an eigenvalue and eigenvector represent: variance for linear PCA, feature-space similarity for kernel PCA, and information content for the entropy-based operator, showing that this distinction determines how spectral results should be interpreted biomedically. The formalism unifies linear, kernel, and information-theoretic correlation analysis within a single operator-algebraic framework whose spectrum is directly interpretable as information content. In biomedical terms, the entropy-based operator indicates that this benchmark’s molecular organisation is dis-tributed across several interconnected, non-linear regulatory axes, consistent with distinct HER2-related, oncogenic signalling and apoptosis-related programmes.

We present a quantum-inspired model that embeds biomedical observables as state vectors in a Hilbert space, enabling the application of the full spectral theory of Hermitian operators and the identification of the system’s natural degrees of freedom as the eigenmodes of a constructed operator, for the analysis of high-dimensional, multifactorial, strongly correlated biomedical systems in which linear reductionist approaches are often insufficient to capture the underlying regulatory structure. Pairwise dependencies between variables are encoded in a Hermitian correlation operator whose off-diagonal elements are generalised mutual information quantities, estimated from joint and marginal Shannon entropies, providing consistent estimates for continuous variables without parametric assumptions. Diagonalisation of this operator yields eigenvalues that quantify the magnitudes of independent biomedical drivers and eigenvectors that identify the corresponding collective modes. Large eigenvalues correspond to dominant regulatory dimensions, while the full eigenvalue spectrum provides compact scalar measures of structural complexity, informational redundancy, and effective dimensionality. Unlike kernel PCA, which requires specification of a kernel function, and unlike linear PCA, which is restricted to second-order statistics, the proposed formalism captures nonlinear and non-Gaussian dependencies within a rigorous operator-algebraic framework whose eigenvalue spectrum is interpretable in terms of information content. We validate the model on a breast cancer gene expression benchmark spanning four molecular subtypes (three breast cancer subtypes and normal tissue), where it resolves five data-driven eigenmodes, two more than linear PCA, while three kernel PCA variants independently confirm the same subtype ordering as an intrinsic property of the data manifold, unifying linear, kernel, and information-theoretic correlation analysis within a single operator-algebraic framework. Collectively, these results indicate that the molecular organisation of the analysed benchmark is not driven by a small number of mutually independent variables but is instead distributed across several interconnected, nonlinear regulatory dimensions, underscoring the added biomedical interpretive value of the entropy-based operator relative to linear and kernel PCA.