Bub and Clifton showed that the operational content of quantum orthogonality relations cannot be recovered from classical spatial geometry without additional interpretive assumptions not present in R3.

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Bub and Clifton(as authors of the research being referenced): David Bub and Rob Clifton are physicists and philosophers of science who worked together on problems in quantum mechanics, particularly about what quantum theory tells us about reality.
Classical spatial geometry(as the framework being tested): The ordinary geometry you learn in school (points, lines, angles, shapes) based on how we experience space in everyday life, as opposed to quantum geometry.
Interpretive assumptions(as additional requirements needed beyond geometry): Extra ideas or rules you have to add when interpreting something, because the raw facts alone don't tell you everything you need to know.
Operational content(as what can or cannot be recovered from geometry): The practical, measurable meaning of something—what you can actually observe or test in an experiment, rather than abstract theory.

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