IMSc Webinar

Observing a changing Hilbert-space inner product

Barry Sanders

University of Calgary

In quantum mechanics, physical states are represented by rays in Hilbert space, which is a vector space imbued by
an inner product whose physical meaning arises as the overlap for a pure state (description of preparation) and
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.
[Based on the joint work written in collaboration with Salini Karuvade and Abhijeet Alase, published in:
Phys. Rev. Research 4, 013016 (2022)]