The laws of physics that govern the microscopic world are called quantum theory, and the basic unit of information contained in the microstructure of matter is called the qubit.String theory is a field that aims to build a unified theory of the universe by fusing the theory of gravity (universal gravitational force, general relativity) and quantum theory.Recently, the new idea that "the universe in gravity theory can be regarded as an aggregate of qubits" is supported and actively studied in this field.

　The Kasa-Takayanagi formula discovered in 2006 was the impetus for this idea.This is "the amount of information of the qubit (correlation between A and B) shared between the two objects A and B is equal to the minimum cross-sectional area of ​​the universe (Note) corresponding to the object". ..However, there is a limitation that the amount of information can be calculated correctly by this formula only when there is no object other than A and B (pure state).

　It is known that a tunnel connecting these can be created in the area of ​​A and B, and the information of A and B is reflected in the internal space (called Entanglement Wedge) of this tunnel.In this study, we have found a significantly generalized formula that can be applied even in the presence of objects other than A and B (mixed state).It states that "the amount of qubit information (purified entanglement) shared between A and B is equal to the minimum cross-sectional area of ​​the tunnel connecting A and B."

　This formula provides a new tool to connect the theory of qubits and the theory of gravity, and is expected to be useful for further understanding of string theory and its application to quantum information theory.

Note: The anti-de Sitter universe is a universe with a negative cosmological constant (dark energy).

Paper information:[Nature Physics]: Entanglement of purification through holographic duality