Quantum Theoretical Approaches and Causality

Aslan Alwi, Munirah, Munirah

Quantum Causal Algebra for Data Representation introduces a new mathematical framework that replaces statistical correlation with quantum causal influence as the foundation of representation learning. Classical data analysis relies on symmetric covariance or correlation matrices, but classical causality is fundamentally directional and incompatible with spectral methods such as PCA. This paper proposes the Quantum Causal Matrix (QCM)—a Hermitian operator encoding causal influence through quantum process matrices, entanglement, and indefinite causal order. We further define the Quantum Causal Tensor (QCT) for higher-order causal structures and develop Quantum Causal PCA (QC-PCA) as a generalization of classical PCA in Hilbert space. This work establishes a novel operator-theoretic and geometric foundation for causal data analysis, bridging quantum information, tensor algebra, and machine learning.

James Paul Wesley

Jincheng Zhang

This paper introduces the concept of the Quantum State Causal Surface (QSCS), a novel theoretical framework proposing that causality may not be solely confined to spacetime but can manifest within the intrinsic structure of quantum states. Traditional understandings of causality are rooted in the temporal and spatial dimensions. The QSCS posits the existence of a causal surface residing within the quantum state space itself. This surface dictates the relationships between quantum events, determining which states can influence others. The core of the theory relies on multi-qubit causal experiments designed to probe this internal causality. The potential implications of discovering causality independent of spacetime are profound, suggesting a fundamental shift in our understanding of the universe and could potentially lead to breakthroughs with significant Nobel Prize potential. This paper lays out the theoretical foundations of the QSCS, outlining its key components and proposing a methodology for experimental verification.

James T. Cushing

Issam Ibnouhsein, Alexei Grinbaum

Reconstructions of quantum theory usually implicitly assume that experimental events are ordered within a global causal structure. The process matrix framework accommodates quantum correlations that violate an inequality verified by all causally ordered correlations. Using a generalized probabilistic framework, we propose three principles constraining bipartite correlations to the quantum bound. Our approach highlights the role of a measure of dependence other than mutual information for an information-theoretic reconstruction of causal structures in quantum theory.

Henry F. Birkenhauer