The Quantum No-Stretching: A geometrical interpretation of the no-cloning theorem

TL;DR

This paper explores the limitations of transferring space rotations between quantum spins, establishing a no-stretching theorem that generalizes the no-cloning principle for quantum information.

Contribution

It introduces a geometrical interpretation of the no-stretching theorem, deriving optimal transformations and linking it to the no-cloning theorem for qubits.

Findings

No-stretching operation is only possible when l=j.

Optimal stretching transformation is derived for l>j.

For qubits, no-stretching is equivalent to no-cloning.

Abstract

We consider the ideal situation in which a space rotation is transferred from a quantum spin j to a quantum spin l different from j. Quantum-information theoretical considerations lead to the conclusion that such operation is possible only for lj. For l>j the optimal stretching transformation is derived. We show that for qubits the present no-stretching theorem is equivalent to the usual no-cloning theorem.