2019/06/30 by Chia-Yi Ju, Adam Miranowicz, Guang-Yin Chen +1 · 1 citation
Mathematics · Physics and Astronomy · #Classical mechanics #Formalism (music) #Hermitian matrix #Mathematics #Open quantum system #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum dynamics #Quantum entanglement #Quantum mechanics #Quantum process #Quantum state #Theoretical physics #Topological Materials and Phenomena #quant-ph
paper · pdf · doi:10.1103/physreva.100.062118
published as Phys. Rev. A 100, 062118 (2019) · 18 pages; title changed; typos fixed; references fixed
openalex publication_date 2019/12/16 · arxiv created 2019/12/17 · arxiv updated 2019/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Recently, apparent nonphysical implications of non-Hermitian quantum mechanics (NHQM) have been discussed in the literature. In particular, the apparent violation of the no-signaling theorem, discrimination of nonorthogonal states, and the increase of quantum entanglement by local operations were reported, and therefore NHQM was not considered as a fundamental theory. Here we show that these and other no-go principles (including the no-cloning and no-deleting theorems) of conventional quantum mechanics still hold in finite-dimensional non-Hermitian quantum systems, including parity-time symmetric and pseudo-Hermitian cases, if its formalism is properly applied. We have developed a modified formulation of NHQM based on the geometry of Hilbert spaces which is consistent with the conventional quantum mechanics for Hermitian systems. Using this formulation the validity of these principles can be shown in a simple and uniform approach.