Is Bayes theorem applicable to all quantum states?

TL;DR

This paper investigates the applicability of Bayes theorem within quantum probability, demonstrating it does not hold for nonfactorizable entangled quantum states, thus highlighting limitations of classical probabilistic reasoning in quantum contexts.

Contribution

The paper shows that Bayes theorem cannot be applied to nonfactorizable entangled quantum states, revealing a fundamental limitation of classical probability in quantum theory.

Findings

Bayes theorem is not applicable to nonfactorizable quantum entangled states.

Classical probability axioms have limited applicability in quantum theory.

Quantum entanglement challenges classical probabilistic reasoning.

Abstract

Reconsidering the already known important question that whether all the axioms and theorems in classical theory of probability are applicable to probability functions in quantum theory, we want to show that the so-called Bayes theorem isn't applicable to nonfactorizable quantum entangled states.