Department of Physics, Graduate School of Science
Quantum mechanics and general relativity, the cornerstones of modern physics, become inconsistent with each other in extreme cases, such as within black holes. The key to solving this mystery is the "AdS/CFT correspondence," which suggests that a theory of quantum gravity in an Anti-de Sitter (AdS) spacetime is equivalent to a quantum field theory without gravity on the boundary of that spacetime. Research over the past two decades, beginning with the Ryu-Takayanagi formula, has revealed a strong connection between the quantum information and quantum computational aspects of the boundary's quantum theory and the geometric properties of the quantum gravity theory.
One of the areas that caught most attention is the analysis of the geometric properties of black holes using quantum complexity. It is known that after a black hole forms, its internal volume continues to grow for a very long time. In quantum theory, the physical quantity that possesses a similar property of long-term growth is nothing other than quantum complexity. Therefore, from the perspective of the AdS/CFT correspondence, it is conjectured that some correspondence must exist between the internal volume of a black hole and quantum complexity.
However, as multiple definitions of quantum complexity exist, it is not yet known which definition should correspond to the internal volume. My research involves quantitatively analyzing these different definitions of quantum complexity and comparing them with the properties of black holes. By studying this, the relationships between different definitions of complexity may also be clarified in some content.