Asymmetric cloning in quantum information theory

TL;DR

This thesis applies advanced representation theory, especially Schur-Weyl duality, to analyze quantum cloning and entanglement, offering new insights into the constraints and capabilities within quantum information processing.

Contribution

It introduces novel applications of Schur-Weyl duality to quantum cloning and entanglement problems, extending understanding of the no-cloning theorem and quantum system representations.

Findings

Enhanced understanding of quantum cloning constraints

Application of representation theory to entanglement problems

Extensions of Schur-Weyl duality in quantum information

Abstract

This thesis investigates quantum cloning and related quantum entanglement problems using core concepts of representation theory, in particular those associated with the symmetric group. The research explores Schur-Weyl duality and its extensions, which allow efficient representation and manipulation of quantum systems, serving as a valuable tool for quantum information theory. A primary application of Schur-Weyl duality is the quantum cloning problem, which is studied for both the $1 \to 2$ and the more general $1 \to N$ cases, providing new insights into the constraints imposed by the no-cloning theorem. The investigation extends to a more general quantum entanglement problem on a complete graph.