Do we loose information when we project a manifold.

For example, do we loose information about the manifold i.e. Earth (Globe) when we project it to a chart in the book (using maybe stereographic, mercator or any other method)

Similarly, we should be loosing information while we create a Bloch sphere for a 2 state system in Quantum Mechanics which is also a Projected space from a higher dimension i.e. 4 dim.

Also, is there a way to quantify this information loss, if there is any?

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