Can quantum entangled states collapse spontaneously?

We investigate the assumption that quantum entangled states Ψ do spontaneously collapse into a mixture of the product states occurring in the Schmidt decomposition of Ψ. We prove that this assumption introduces new observables in quantum mechanics. In particular mixtures that are indistinguishable according to standard quantum mechanics, would be distinguishable. Since such mixtures can be prepared at an arbitrarily large distance, the assumption activates the quantum non-locality.