Chia-Yi Ju

Department of Physics
National Chung Hsing University
Taiwan

The Geometries of Quantum States and the No-Go Theorems

In the past decade, some studies have shown that many of the no-go theorems are violated in non-Hermitian quantum systems. Since these no-go theorems are closely related to some fundamental physics principles, the violations lead to the conclusion that non-Hermitian quantum systems can only be effective systems, at best, rather than fundamental ones. In this talk, we will show that the Schroedinger's equation hints that it might be the ``conventional'' Hilbert spaces of quantum mechanics that is unsuitable for the no-go theorems in non-Hermitian cases. With this observation, the geometry of the quantum states is generalized in a natural way by making it compatible with the Schroedinger's equation. The no-go theorems are proven to be violation-free with the generalized geometries. Hence, the non-Hermitian quantum mechanics can still be fundamental.

[1] C.-Y. Ju, A. Miranowicz, G.Y. Chen, F. Nori, No-Go Theorems in Non-Hermitian Quantum Mechanics, arXiv:1906.08071.
[2] Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, Parity-time symmetry and exceptional points in photonics, Nat. Mater. 18, 783 (2019).