Under preparation independence, an ontological model of a quantum system reproducing exact quantum quantum measurement probabilities cannot assign overlapping preparation measures to distinct pure states. An exclusion quantum measurement on independent copies makes every outcome impossible for one possible preparation; a common ontic region would require every response to vanish there. Thus the conclusion is a psi-ontic model, not a blanket exclusion of hidden variables or all informational interpretations.
If two pure quantum states overlap by , their -copy states have overlap . Each block spans an effective qubit, with orthonormal basis and . Applying the two-block PBR exclusion measurement for zero and plus uses independently prepared copies. A common single-copy ontic overlap of positive mass remains positive under this finite tensor power.
The product preparations are excluded respectively by the orthonormal vectors , , and , written in the computational basis. Each vector has zero inner product with its labelled preparation. This projective measurement gives antidistinguishable quantum states and drives the two-copy PBR theorem contradiction.
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The Pusey–Barrett–Rudolph (PBR) theorem is a result in quantum mechanics that addresses the interpretation of quantum states and their relationship to physical reality. Proposed by Matthew Pusey, Jonathan Barrett, and Nicolas Rudolph in 2012, the theorem argues against certain interpretations of quantum mechanics, particularly those that claim that quantum states merely represent knowledge about an underlying reality rather than representing a physical reality itself.