Regular Article

Two-qubit mixed states and teleportation fidelity: purity, concurrence, and beyond

¹ Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, Odisha, India
² Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India

^a e-mail: sumit@iopb.res.in

Received: 29 May 2018
Received in final form: 3 August 2018
Published online: 16 October 2018

Abstract

To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fidelity of a teleported state depends on the resource state purity and entanglement, as characterized by concurrence. Concurrence and purity are functions of state parameters. However, it turns out that a state with larger purity and concurrence, may have comparatively smaller fidelity. By computing teleportation fidelity, concurrence and purity for two-qubit X-states, we show it explicitly. We further show that fidelity changes monotonically with respect to functions of parameters – other than concurrence and purity. A state with smaller concurrence and purity, but larger value of one of these functions has larger fidelity. These functions, thus characterize nonlocal classical and/or quantum properties of the state that are not captured by purity and concurrence alone. In particular, concurrence is not enough to characterize the entanglement properties of a two-qubit mixed state.