The quadratic-generation conjecture for matroid toric ideals

Let $M$ be a matroid and let $I_M$ be its toric ideal. A quadratic binomial in $I_M$ is a binomial homogeneous of degree two in the base variables. The quadratic-generation conjecture. For any matroid $M$, the toric ideal $I_M$ is generated by quadratic binomials. The source separates this assertion from the stronger symmetric-exchange generation claim; it states that this conjecture and the companion exchange-generation conjecture are both still open and together imply White's conjecture.