Process-theoretic characterisation of the Hermitian adjoint
  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. Also, we show that for general process theories, which all admit a diagrammatic representation, this physical principle induces a reflection operation. 
John Selby and Bob Coecke
quant-ph