Speaker
Description
The emergence of spacetime geometry from quantum degrees of freedom is a central problem in quantum gravity and holography. We propose an approach based on optimal transport, in which the Wasserstein distance defines a geometry on the space of quantum states. In simple quantum-mechanical models, this approach yields an emergent holographic direction parameterized by an energy-like coordinate. Also, in a quantum-chaotic system, it turns out that stronger quantum chaos reduces the number of effective dimensions of emergent space. This suggests that quantum chaos may underlie the dimensional reduction needed for an emergent holographic interpretation. These observations motivate optimal transport as a new tool for studying holography and quantum chaos.