No-Go Theorems in Non-Hermitian Quantum Mechanics.

Recently, apparent non-physical implications of non-Hermitian quantum mechanics (NHQM) have been discussed in the literature. In particular, the apparent violation of the non-signaling theorem, discrimination of non-orthogonal 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 are indeed satisfied in any NHQM 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.