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

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Vol. 72; no. 10
• Main Authors: Nandi, Sumit, Datta, Chandan, Das, Arpan, Agrawal, Pankaj
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2018; Springer Nature B.V
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Molecular; Optical and Plasma Physics; Parameters; Physical Chemistry; Physics; Physics and Astronomy; Properties (attributes); Purity; Quantum entanglement; Quantum Information Technology; Quantum Physics; Quantum teleportation; Quantum theory; Qubits (quantum computing); Regular Article; Spectroscopy/Spectrometry; Spintronics; Quantum Information
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/e2018-90252-2

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. Graphical abstract