Entanglement in non-Hermitian quantum theory

ARUN K PATI

Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India

E-mail: akpati@iopb.res.in

Abstract. Entanglement is one of the key features of quantum world

that has no classical counterpart. This arises due to the linear

superposition principle and the tensor product structure of the

Hilbert space when we deal with multiparticle systems. In this

paper, we will introduce the notion of entanglement for quantum

systems that are governed by non-Hermitian yet $\cal PT$-symmetric

Hamiltonians. We will show that maximally entangled states in usual

quantum theory behave like non-maximally entangled states in $\cal

PT$-symmetric quantum theory. Furthermore, we will show how to

create entanglement between two $\cal PT$qubits using non-Hermitian

Hamiltonians and discuss the entangling capability of such

interaction Hamiltonians that are non-Hermitian in nature.

Keywords. Entanglement; non-Hermitian Hamiltonians; $\cal PT$ symmetry.

PACS Nos 03.65.-w; 03.65.Ca; 03.67.-a