In quantum mechanics, physical states are represented by rays in Hilbert space H, which is a vector space imbued by an inner product ⟨|⟩, whose physical meaning arises as the overlap ⟨φ|ψ⟩ for |ψ⟩ a pure state (description of preparation) and ⟨φ| a projective measurement. However, current quantum theory does not formally address the consequences of a changing inner product during the interval between preparation and measurement. We establish a theoretical framework for such a changing inner product, which we show is consistent with standard quantum mechanics. Furthermore, we show that this change is described by a quantum operation, which is tomographically observable, and we elucidate how our result is strongly related to the exploding topic of PT-symmetric quantum mechanics. We explain how to realize experimentally a changing inner product for a qubit in terms of a
qutrit protocol with a unitary channel.