Instability, Isolation, and the Tridecompositional Uniqueness Theorem

The tridecompositional uniqueness theorem of Elby and Bub (1994) shows that a wavefunction in a triple tensor product Hilbert space has at most one decomposition into a sum of product wavefunctions with each set of component wavefunctions linearly independent. I demonstrate that, in many circumstances, the unique component wavefunctions and the coefficients in the expansion are both hopelessly unstable, both under small changes in global wavefunction and under small changes in global tensor product structure. In my opinion, this means that the theorem cannot underlie lawlike solutions to the problems of the interpretation of quantum theory. I also provide examples of circumstances in which there are open sets of wavefunctions containing no states with various decompositions.