#### IMSc Webinar

#### Operational Foundations of PT-Symmetric and Quasi-Hermitian Quantum Theory

#### Abhijeet Alase

##### University of Sydney, Australia

*PT-symmetric quantum theory was originally proposed with the*

aim of extending standard quantum theory by relaxing the Hermiticity

constraint on Hamiltonians. However, no such extension has been formulated

that consistently describes states, transformations, measurements and

composition, which is a requirement for any physical theory. We aim to

answer the question of whether a consistent physical theory with

PT-symmetric observables extends standard quantum theory. We answer this

question within the framework of general probabilistic theories, which is

the most general framework for physical theories. We construct the set of

states of a system that result from imposing PT-symmetry on the set of

observables, and show that the resulting theory allows only one trivial

state. We next consider the constraint of quasi-Hermiticity on observables,

which guarantees the unitarity of evolution under a Hamiltonian with

unbroken PT-symmetry. We show that such a system is equivalent to a

standard quantum system. Finally, we show that if all observables are quasi

Hermitian as well as PT-symmetric, then the system is equivalent to a real

quantum system. Thus our results show that neither PT-symmetry nor quasi

Hermiticity constraints are sufficient to extend standard quantum theory consistently.

This webinar will be based on:

Abhijeet Alase, Salini Karuvade, Carlo Mria Scandolo

"The operational foundations of PT-symmetric and quasi-Hermitian quantum theory."

Journal of Physics A: Mathematical and Theoretical 55.24 (2022): 244003.

scholar.google.com/scholar?cluster=14804058696554185428

Zoom link of the talk:-

zoom.us/j/96286449863

Meeting ID: 962 8644 9863

Passcode: 200887

Done