Clonagem quântica de qudits

Abstract

One of the main differences between classical and quantum information is that the former can be replicated. That is, we can easily obtain copies from classical bits but, while dealing with qubits and qudits, we are subject to Quantum Mechanic¿s rules, which determines that arbitrary quantum states cannot be perfectly copied. Still, we can use the so called Quantum Cloning Machines to try and obtain approximate copies with the highest Fidelity or perfect copies with bigger success rates. Those machines are also tools that can be used to study a variety of tasks like, for example, the security analysis of quantum cryptography protocols and quantum state discrimination. One of the aims of this work is to present a brief review of some research about the quantum cloning theory as well as previous discussions on non-cloning theorem, including Herbert¿s proposal for superluminal communication. This work¿s second aim is to analyse an experimental realization and is based on the optical implementation of the so-called optimal universal quan- tum cloning machines for hybrid ququarts encoded in the polarization and orbital angular momentum degrees of freedom of photons, proposed by Na- gali et al.{Phys. Rev. Lett. 105, 073602 }. The implementation is based on the Hong-Ou-Mandel effect and on the photons produced by Parametric Down Conversion. We presented all the concerned theory and obtained the theoretical Fidelity curve predicted by using the quantum state propagation through the optical elements present on the circuit. We also proposed an implementation change for the use of qudits encoded in transversal momen- tum.