Bernstein's socks and polynomial-time provable coherence

TL;DR

This paper explores a polynomial-time provable coherence framework for desirable gambles, demonstrating how Bernstein polynomials with Krivine-Vasilescu certificates can model entanglement phenomena with classical coins.

Contribution

It extends the bounded rationality approach to desirable gambles by incorporating Bernstein polynomials and Krivine-Vasilescu certificates, linking classical models to quantum-like entanglement.

Findings

Bernstein polynomials can be used within this framework.

The model can simulate entanglement with classical coins.

Polynomial-time provability is maintained in the model.

Abstract

We recently introduced a bounded rationality approach for the theory of desirable gambles. It is based on the unique requirement that being non-negative for a gamble has to be defined so that it can be provable in polynomial-time. In this paper we continue to investigate properties of this class of models. In particular we verify that the space of Bernstein polynomials in which non-negativity is specified by the Krivine-Vasilescu certificate is yet another instance of this theory. As a consequence, we show how it is possible to construct in it a thought experiment uncovering entanglement with classical (hence non quantum) coins.