Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation

TL;DR

This paper reviews recent theoretical advances in quantum entanglement, focusing on criteria for separability, measures like concurrence and tangle, and their implications for teleportation fidelity and entanglement distillation.

Contribution

It provides a comprehensive overview of recent results in quantum entanglement theory, including new criteria and measures relevant for quantum information tasks.

Findings

Separable criteria based on Bloch representation and entanglement witnesses

Lower bounds and properties of concurrence and tangle

Relation of fully entangled fraction to teleportation fidelity

Abstract

Quantum entanglement plays crucial roles in quantum information processing. Quantum entangled states have become the key ingredient in the rapidly expanding field of quantum information science. Although the nonclassical nature of entanglement has been recognized for many years, considerable efforts have been taken to understand and characterize its properties recently. In this review, we introduce some recent results in the theory of quantum entanglement. In particular separability criteria based on the Bloch representation, covariance matrix, normal form and entanglement witness; lower bounds, subadditivity property of concurrence and tangle; fully entangled fraction related to the optimal fidelity of quantum teleportation and entanglement distillation will be discussed in detail.