Complex extension of Wigner's theorem

Abstract

Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed, we obtain the following complex generalisation of Wigner's theorem: a holomorphically projective (complex geodesic-curves preserving) transformation on a quantum state space must be generated by a Hamiltonian that is not necessarily Hermitian.

13 pages, no figure

References in corpus (3)

• Mixed-state evolution in the presence of gain and loss
• Wave packet evolution in non-Hermitian quantum systems
• Information Geometry of Complex Hamiltonians and Exceptional Points

Cited by in corpus (1)

• Evolution speed of open quantum dynamics