Entanglement of bipartite states and quantum teleportation: an introduction

TL;DR

This paper provides an accessible overview of bipartite entanglement, Bell's theorem, and quantum teleportation, emphasizing their roles in quantum information processing.

Contribution

It introduces key concepts like Bell's theorem, Schmidt decomposition, and the Peres-Horodecki criterion, illustrating their application in quantum teleportation.

Findings

Explanation of Bell's theorem and its derivation by CHSH

Discussion of Schmidt decomposition and Peres-Horodecki criterion

Description of a quantum teleportation protocol

Abstract

There has been spectacular progress in the field of quantum information in recent decades. The development of this field highlights the importance of the role of entanglement in quantum computing, quantum teleportation and quantum cryptography. These notes serve to provide a gentle introduction to the entanglement of bipartite states. In these notes, we introduce Bell's theorem in the form derived by Clauser, Horne, Shimony and Holt. We discuss the Schmidt decomposition and the Peres-Horodecki criterion in the entanglement of pure and mixed bipartite states. Finally, we describe a teleportation protocol as an illustration of the use of entangled states.