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

TL;DR

This paper investigates how purity, concurrence, and other functions influence teleportation fidelity in two-qubit mixed states, revealing that fidelity depends on more than just purity and entanglement measures.

Contribution

It demonstrates that fidelity is affected by additional state parameters beyond purity and concurrence, highlighting the limitations of these measures in characterizing entanglement.

Findings

Fidelity can decrease even with higher purity and concurrence.

Fidelity varies monotonically with certain functions of state parameters.

Concurrence alone does not fully characterize entanglement in two-qubit states.

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.