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Mark_Friedenbach comments on If Many-Worlds Had Come First - Less Wrong
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? What aspect of measuring an electron's spin is not reversible? Physics at this scale is entirely reversible.
If you define a measurement as an the creation of a (FAPP) irreversible record....then, no.
You can reversibly entangle an electron's spin to the state of some other small quantum system, that's not questioned by any interpretation of QM, but unless this entanglement propagates to the point of producing a macroscopic effect, it is not considered a measurement.
It's even worse than that. Zurek's einselection relies on decoherence to get rid of non-eigenstates, and reversibility is necessarily lost in this (MWI-compatible) model of measurement. There is no size restriction, but the measurement apparatus (including the observer looking at it) must necessarily leak information to the environment to work as a detector. Thus a reversible computation would not be classically detectable.
Which is why the experiment as described in the link I provided requires an artificial intelligence running on a reversible computing substrate to perform the experiment in order to provide the macroscopic effect.
That is, it would require inverting the thermodynamic arrow of time.