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Is there a way to obtain a value from the qubit once measured between a predefined boundary (for example 15 < x < 20) and if so, does this correspond to some restriction on the surface of the Bloch sphere for some geometric interpretation?

If not, I'd appreciate any feedback on the matter. As I am not a physicist by profession, please excuse my ignorance. Thanks for your kindness. Also, if any follow up questions are needed by me for clarification, please do not hesitate to ask I will respond promptly.