Foundations of Physics 47 (9):1191-1207 (2017)

We show that the physical principle, “the adjoint associates to each state a ‘test’ for that state”, fully characterises the Hermitian adjoint for pure quantum theory, therefore providing the adjoint with operational meaning beyond its standard mathematical definition. Moreover, we demonstrate that for general process theories, which all admit a diagrammatic representation, this physical principle induces a diagrammatic reflection operation.
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DOI 10.1007/s10701-017-0102-7
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