Journal
PHYSICAL REVIEW A
Volume 100, Issue 6, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.100.062118
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Funding
- Ministry of Science and Technology, Taiwan [MOST 108-2112M-005-005]
- MURI Center for Dynamic Magneto-Optics via the Air Force Office of Scientific Research (AFOSR) [FA9550-14-1-0040]
- Army Research Office (ARO) [W911NF-18-1-0358]
- Asian Office of Aerospace Research and Development (AOARD) [FA2386-18-1-4045]
- Japan Science and Technology Agency (JST) (Q-LEAP program)
- Japan Science and Technology Agency (JST) (CREST) [JPMJCR1676]
- Japan Society for the Promotion of Science (JSPS) (JSPS-RFBR) [17-52-50023]
- Japan Society for the Promotion of Science (JSPS) (JSPS-FWO) [VS.059.18N]
- RIKENAIST Challenge Research Fund
- Foundational Questions Institute (FQXi)
- NTT PHI Laboratory
- National Center for Theoretical Sciences
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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.
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