The Dichotomy of Belief: Clarifying the "Subject-Object Consistency" Question in Quantum Bayesianism from a Computational Complexity Perspective

zihaochen.dynamic@wszim.edu.pl This paper addresses a persistent philosophical challenge in Quantum Bayesianism (QBism): how can subjective beliefs produce objectively consistent predictions? We identify the root cause as a confusion about the concept of "belief" and propose a crucial dichotomy between generalized belief (the consensus quantum state determined by rational update rules given public experimental data) and specific belief (an individual's personal probability assignment). We argue for the necessity of generalized belief by demonstrating that quantum processes are inherently strongly path-dependent, derived from relativistic causality and quantum contextuality (Kochen-Specker theorem). To quantify this dependency, we construct a Path Information Processing Computational Model and prove, via reduction to known #P-hard problems, that computing quantum measurement outcome probabilities from complete historical information is #P-hard. This establishes a principle-based epistemic boundary. Under this boundary constraint, the wave function emerges as the optimal generalized belief - an efficient compression scheme for statistical correlations rather than an ontological entity. Experiments thus validate this public predictive tool, not individual subjective hunches. The diversity of specific beliefs remains compatible with objective consistency as long as they are rationally updated within the generalized belief framework. This work clarifies QBism's core concepts, resolves the subject-object consistency paradox, and provides a unified perspective based on computational complexity for understanding the instrumental status of the quantum state. The results have implications for quantum foundations, epistemology, and the philosophy of science. Keywords: Quantum Bayesianism, Quantum foundations, Computational complexity, Quantum measurement, Contextuality, Path dependence, Kochen-Specker theorem, Epistemic boundaries