Relative Entropy and Proximity of Quantum Field Theories

Understand

We study the question of how reliably one can distinguish two quantum field theories (QFTs).

• Each QFT defines a probability distribution on the space of fields.
• The relative entropy provides a notion of proximity between these distributions and quantifies the number of measurements required to distinguish between them.
• In the case of nearby conformal field theories, this reduces to the Zamolodchikov metric on the space of couplings.