The development of quantum theory and the use of some specific quantum features such as the superposition principle and entanglement have allowed a substantial development of information and computation theory. The capability to extract information from an unknown state is of crucial interest in the development of quantum information protocols. The standard approach used to reconstruct the density matrix of an unknown state is the so-called quantum state tomography. However, this approach becomes inflexible increasing the dimensionality of the quantum state. Indeed, the number of measurements needed to extract the stored information and, so, the employed copies of the target state increase exponentially. On the other hand, Machine Learning techniques have been deeply developed, in recent years. Therefore, several approaches have been proposed combining this tool with the quantum information field. Among the others, Reinforcement Learning algorithms represent a powerful tool to reconstruct unknown quantum states in automatized experiments as demonstrated for 2-dimensional states encoded in the polarization degree of freedom of single photons. A fundamental step is the application of such techniques also for quantum states with higher dimensions since they represent key elements able to enhance several quantum information tasks.
This project aims exactly at reaching this goal by theoretically and experimentally generalizing the Reinforcement Learning to the case of d-dimensional states. To this purpose, the target state can be encoded in the orbital angular momentum degree of freedom of photon and the semi-automatic protocol can be implemented by using motorized waveplates and a device that is able to couple the orbital angular momentum and the polarization of the light. The funding will be employed to buy two motorized precision rotational stages for the waveplates, which will be necessary to automatize the learning protocol.
The innovation aspect of this project is related to the development of a flexible and semi-automatic protocol able to reconstruct an unknown d-dimensional state by using a number of resources lower than that envisaged in the tomography process. Experimentally, due to challenging preformation of state tomography in such high dimensional framework and to the technical difficulty in the manipulation and detection of the OAM degree of freedom, several research activities have been conducted. However, the pursued results are limited or to the classification and regression of specific OAM input states or to the development of more flexible and universal protocols intended for the analysis and reconstruction of qudit state encoded in different physical settings. The main focus of the current project is to merge the last two aspects and, consequently, to develop a flexible protocol able to extract the information stored in generic high dimensional states encoded in the OAM. As stated before, the Quantum Information Lab has already performed different experiments in this topic and it has accumulated experience in the manipulation of the OAM and in the employment of Machine Learning algorithms. Therefore, we are very confident about the possibilities to bring a significant contribution to this topic. The desirable fulfillment of this result could cause a fundamental step forward in the development of quantum information and cryptography protocols. Moreover, it could corroborate the fundamental position that the Machine Learning algorithm occupies in the development of the quantum information field.