I'm not sure what you mean by "proposing what continuity holds for the quantum system". There are a number of results about how measurements of an individual i

I'm not sure what you mean by "proposing what continuity holds for the quantum system". There are a number of results about how measurements of an individual infinite-dimensional quantum system can be approximated to arbitrary degree by an arbitrarily large finite-dimensional system. This new result seems to suggest that for joint entangled systems there's a "buffer" between measurement results obtained by having arbitrarily many dimensions, and by having infinite dimensions. I was wondering how practical it could be to actually do an experiment and verify that the buffer line is crossed.