it’s just that it’s unclear to me how seriously we should take them at this stage
Well, categorical quantum mechanics is a program under developement since 2008, and it gives you a quantum framework in any computational theory with enough symmetries (databases, linguistics, etc). It spawned quantum programming languages and a graphical calculus. So I think it’s pretty succesful and has to be taken seriously, albeit it’s far from being complete (it lacks a unified treatment of infinite systems, for example).
Well, categorical quantum mechanics is a program under developement since 2008, and it gives you a quantum framework in any computational theory with enough symmetries (databases, linguistics, etc).
It spawned quantum programming languages and a graphical calculus. So I think it’s pretty succesful and has to be taken seriously, albeit it’s far from being complete (it lacks a unified treatment of infinite systems, for example).