Geometric bounds for approximate quantum error correction and a few words about holography

• Ano de defesa: 2022
• Autor(a) principal: Fiusa, Guilherme Camargo
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: AdS/CFT; Correção de erros; Quantum error correction; Quantum information theory; Quantum resource theory; Teoria de informação quântica; Teoria quântica de recursos
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/76/76134/tde-14102022-090414/

In this work, we investigate some applications of quantum information theory motivated by high-energy physics. There is strong evidence suggesting that entanglement is deeply connected with the geometry of spacetime, which leads to surprising applications of quantum information theory in the AdS/CFT correspondence and holography. We start by reviewing the fundamental concepts of the AdS/CFT correspondence which play a key role in bulk-boundary reconstruction, in particular, we explore some features which suggest that one must interpret the encoding of information in the correspondence as a quantum errorcorrecting code. We discuss the fundamentals of error correction, exploring the formalisms of operator algebra and stabilizer codes. Then, we establish the concrete connection between the two main concepts by showing examples of quantum error-correcting codes that serve as a toy model for AdS/CFT. We illustrate how the 3-qutrit code and the HaPPY code can be powerful tools to explore the correspondence analytically and to solve apparent paradoxes. Following recent results, using quantum error correction, that suggest an intrinsic incompatibility of quantum gravity with global symmetries, we explore approximate error-correcting codes and asymmetric codes as a way to better understand the consequences in a quantum resource-theoretic way. Finally, we discuss our original contribution: geometric bounds for approximate quantum error correction. We calculate our bounds for three typical quantum channels that model the lack of exactness in error correction, namely, dephasing, depolarizing, and amplitude damping channels. The implications of our bounds for AdS/CFT are somewhat elusive; nonetheless, we provide a new approach to benchmark approximations in error correction performance, which may be of high interest for AdS/CFT and its corresponding absence of global symmetries.