Observing a changing Hilbertspace inner product
Abstract
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 PTsymmetric 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.
 Publication:

Physical Review Research
 Pub Date:
 January 2022
 DOI:
 10.1103/PhysRevResearch.4.013016
 arXiv:
 arXiv:2101.00015
 Bibcode:
 2022PhRvR...4a3016K
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 12 pages, 4 figures