Entanglement witnesses with tensor networks: characterizing entanglement in large systems

• Autor(a) principal: Lucas Vieira Barbosa
• Data de Publicação: 2019
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/31439
• topic: Entanglement; Entanglement witnesses; Entanglement in pure states; Negative partial transpose; Semidefinite programming; Tensor networks; Matrix product state; Matrix product operator; Density matrix renormalization group; Partial transpose; Informação quântica; Teoria quântica

Entanglement is certainly one of the most fascinating phenomena observed in Nature, and even after decades of research in entanglement theory there is still much to be discovered and understood. In particular, there are still few results detailing and characterizing the entanglement structure in strongly correlated systems on a large scale, involving a large number of subsystems. The most typical approach for studying in detail the entanglement structure in quantum states has been through the optimization of Entanglement Witnesses, optimized by means of algorithmic techniques such as Semidefinite Programming applied to matrices. However, this matrix description renders the technique computationally nonviable for large scale systems due to the exponential growth of the dimension of the optimization parameters. All these techniques are nonviable for a relatively small number of particles (on the order of n ~ 10^1). For these reasons, Tensor Networks have attracted the attention of researchers over the last decades for being more efficient ways to describe and simulate quantum systems composed of many parts, as they are more natural and efficient descriptions of the quantum correlations between subsystems. However, few progress has been made for the detailed characterization of entanglement in such systems, and the literature still hasn't fully bridged the gap between the two formalisms. In this work, we propose a small step towards the goal of adapting the formalism of entanglement witnesses in a way which is compatible with the description of quantum systems by means of tensor networks, making it possible the characterization of entanglement in large scale systems.