I want to share with you my excitement for this new work:
Computational Complexity and the Nature of Quantum Mechanics
Alessio Benavoli, Alessandro Facchini, Marco Zaffalon
In a previous paper, we derived the axioms of QM from the same rationality principles that underlie the subjective foundation of probability. We were able to show the way QM is similar to classical probability, but we weren’t able to fully grasp the differences between the two theories. Why does entanglement exist? What is entanglement?
To model these differences, Von Neumann changed the logic of the events, while Dirac and Feynman introduced negative probabilities. But why?
In this new work, we believe we have finally answered that question and the why is simple to understand. QM is a theory of computational rationality, that is based on a different notion of non-negativity (that is, the notion for a real-valued function to be non-negative). The reason is purely computational. This different notion of non-negativity allows the inferences in the theory to be computed in polynomial time. Conversely, in the same settings, classical probability is NP-hard. In other words, we have proven that the only physics’ axiom in QM is computational tractability. All the weirdness (different logic of events, negative probabilities, and entanglement) is a simple consequence of that. Moreover, we show that entanglement is a characteristic of computational rationality and we give an example of entanglement outside QM.
There is more, actually QM is a theory of imprecise probability (because we show that, when QM is compatible with classical probability, the density matrix is actually a truncated moment matrix).
The above linked paper is really simple to read and understand. You do not need to know QM.
A longer version can be found here http://arxiv.org/abs/1902.03513
Since you are into quantum mechanics and Bayesian thinking, you might be interested in quantum bayesian networks. Just like classical b nets are a graphical way of displaying the chain rule for **probabilities**, quantum b nets are a graphical way of displaying the chain rule for **probability amplitudes**.
By the way, I am a long time admirer of bnlearn and of its author, Marco Scutari, who also works at SUPSI. This is a link to a blog post of mine about Marco
Thank you Robert for the link