Quantum Teleportation and Von Neumann Entropy

TL;DR

This paper analyzes single qubit quantum teleportation using quantum information theory, focusing on entropy and mutual information changes, revealing insights into the roles of measurement and entanglement in the process.

Contribution

It provides a detailed entropy-based analysis of quantum teleportation, highlighting how measurement and initial state basis affect information flow and entanglement.

Findings

Mutual information $S(B:C)$ becomes non-zero before measurement.

Measurement's role varies with the initial state basis.

Entropic analysis clarifies the emergence of entanglement during teleportation.

Abstract

The single qubit quantum teleportation (sender and receiver are Alice and Bob respectively) is analyzed from the aspect of the quantum information theories. The various quantum entropies are computed at each stage, which ensures the emergence of the entangled states in the intermediate step. The mutual information $S(B:C)$ becomes non-zero before performing quantum measurement, which seems to be consistent to the original purpose of the quantum teleportation. It is shown that if the teleported state $|\psi>$ is near the computational basis, the quantum measurement in $C$-system is dominantly responsible for the joint entropy $S(A,C)$ at the final stage. If, however, $|\psi>$ is far from the computational basis, this dominant responsibility is moved into the quantum measurement of system $A$. A possible extension of our results are briefly discussed.