Conventional Bell Basis in PT-symmetric Quantum Theory

Abstract

Theories defined by non-Hermitian PT-symmetric Hamiltonians exhibit strange and unexpected properties at the classical as well as at the quantum level. In this paper the conventional Bell basis is discussed using the CPT-inner product for a general two-state system in PT-symmetric quantum theory. The conventional Bell basis has many applications in quantum information theory because of the mutual orthogonality, normlization, and maximally entangled degree of each vector in the basis. This paper analyzes four properties of the Bell basis in PT-symmetric quantum theory: CPT-orthogonality, CPT-norm, CPT-entanglement degree and CPT-mutual unbiased property with other maximally entangled bases. The conventional Hermitian Bell states are not CPT-normalized and are not maximally entangled states in PT-symmetric quantum theory. The orthogonality still holds for four of the six pairs of Bell states under the CPT-inner product. Furthermore, the mutually unbiased property with another maximally entangled basis is preserved at the level of twenty five percent.