Quantum cloning and teleportation fidelity in the noncommutative phase-space

TL;DR

This paper explores how noncommutative quantum mechanics affects quantum cloning and teleportation fidelity, providing a covariant formulation and linking standard and noncommutative frameworks for Gaussian states.

Contribution

It extends the no-cloning theorem and teleportation fidelity analysis to noncommutative quantum mechanics using a covariant phase-space approach.

Findings

Reproduces standard QM results within NC framework for Gaussian states

Establishes a covariant formulation for quantum fidelity in NC QM

Suggests a feasible interpretation of NC quantum cloning via teleportation protocols

Abstract

The formulation of the no-cloning theorem in the framework of phase-space noncommutative (NC) quantum mechanics (QM) is examined, and its implications for the computation of quantum cloning probabilities and teleportation fidelity are investigated through the Weyl-Wigner formulation of QM. The principles of QM re-edited in terms of a deformed Heisenberg-Weyl algebra are shown to provide a covariant formulation for the quantum fidelity, through which the results from the no-cloning theorem for the ordinary QM can be reproduced. Besides exhibiting an explicit correspondence between standard and NC QM for Gaussian Wigner functions, our results suggest a feasible interpretation for the NC continuous variable quantum cloning given in terms of quantum teleportation protocols.