Local entangled states certification

Author(s)

Gabriela Ruiz

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin
• Defense date: 2023-08-04

Examining board members

Rafael Luiz da Silva Rabelo; Marcelo de Oliveira Terra Cunha; Leonardo Guerini de Souza

• Advisor: Rafael Luiz da Silva Rabelo

Abstract

Entanglement, Bell non-locality, and Steering, previously considered synonymous, are distinct nonclassical concepts. Although entanglement is necessary, it is not a sufficient condition for the correlations exhibited by a system to be nonlocal and/or steerable, and thus display stronger-than-classical behavior. The exact relationship between these three phenomena is unknown. The problem of checking whether a general quantum state can generate non-local statistics is notoriously difficult. There is little hope of obtaining a systematic analytical tool for answering this question. Therefore, numerical methods have been developed for the partial solution of such problems. In this project, the student used a method that relies on a subset of convex optimization, called semi-definite programming, which was presented in a 2016 article that includes the student's advisor as one of the authors. With this new optimized and generalized method, we were able to investigate and certify the locality of a wide range of entangled quantum states, and obtained improved bounds on the volume of two-qubit states that are both entangled and local. However, this method has limitations and works best with low dimensions and few measurements. Based on the success of Machine Learning techniques on similar problems with many variables, and with several examples already classified by our previous method, we discuss building a model using the Multi-Layer Perceptron method to classify whether states are entangled and local or not (AU)

• FAPESP's process: 21/13798-7 - Certification of local entangled states
• Grantee: Gabriela Ruiz
• Support Opportunities: Scholarships in Brazil - Master