Using the Schmidt Decomposition to Determine Quantum Entanglement

TL;DR

This paper explains how the Schmidt decomposition can be used to identify quantum entanglement and demonstrates its application in quantum teleportation, highlighting its importance in quantum information processing.

Contribution

It introduces the mathematical method of Schmidt decomposition for detecting entanglement and explores its application in quantum teleportation and potential extensions.

Findings

Schmidt decomposition effectively identifies entanglement in quantum systems

Demonstrated the use of entanglement in quantum teleportation

Discussed potential extensions of the Schmidt decomposition method

Abstract

Quantum information theory is a rapidly growing area of math and physics that combines two independent theories, quantum mechanics and information theory. Quantum entanglement is a concept that was first proposed in the EPR paradox. In quantum mechanics, particles can be in superposition, meaning they are in multiple different states at once. It is not until the particle is measured that it is forced into a single state. However, it is possible that particles can be tied to other particles, meaning that the measurement of one particle will determine the measurement of the other particle. Entanglement is at the very core of quantum information theory. It is one of the core pieces that allows for the massive increase in computing power. For this paper, we decided to focus on demonstrating the mathematical method (the Schmidt decomposition) for determining if a system is entangled, and a demonstration of quantum entanglement's use (quantum teleportation) as well as a quick look at how to extend the uses of the Schmidt decomposition.