The Born rule for a fixed projective measurement is the only readout map obeying square-root regularity on Fubini-Study geodesics, the universal readout Cramer-Rao bound, and operational basis calibration.
Any modification of the Born rule leads to a violation of the purification and local tomography principles
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Fixed-PVM Born Rule Uniqueness from Fisher Non-Expansion and Operational Calibration
The Born rule for a fixed projective measurement is the only readout map obeying square-root regularity on Fubini-Study geodesics, the universal readout Cramer-Rao bound, and operational basis calibration.