Thursday, August 11 2022
11:30 - 12:45

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.

Zoom link of the talk:-
Meeting ID: 962 8644 9863
Passcode: 200887

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