Dear SIPTA members,

I want to share with you our excitement for this new work:

Computational Complexity and the Nature of Quantum Mechanics
Alessio Benavoli, Alessandro Facchini, Marco Zaffalon

If you saw my presentation at last Isipta, then you know that, in a previous paper, we derived the axioms of QM from desirability. 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 (for our community). QM is a theory of bounded rationality, that is based on a different notion of non-negativity (the gambles we should always desire). 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 (standard desirability) 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�� bounded rationality and we give an example of entanglement outside QM.

There is more, actually QM is a theory of imprecise probability (whose credal set is defined by 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

Enjoy it!

Alessio