Open Research Index

stalex444/Busch-theorem

Stephanie Alexander

Palomar Registrypalomar/PALOMAR-2026-08-31-000014Aug 31, 2026quant-phscore 0

Kernel-checked proof of Busch's theorem in finite dimension: every generalized probability measure on the effects of a complex matrix algebra — nonnegative on effects, additive whenever a sum of effects is again an effect, normalized at the identity — is represented by a unique density matrix via the trace pairing. Existence and uniqueness are both compared (busch_representation). The result is the uniqueness of the Born rule in the POVM reading; it is valid in every finite dimension (beyond finiteness and decidable equality of the index type, the compared statement assumes only [Nonempty…

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