Entropies in Quantum Field Theory

Jurjen F. Koksma, Tomislav Prokopec, Michael G. Schmidt

Noboru Watanabe

David Blanco

In the last decades, it has been understood that a wide variety of phenomena in quantum field theory (QFT) can be characterised using quantum information measures, such as the entanglement entropy of a state and the relative entropy between quantum states in the same Hilbert space. In this thesis, we use these and other tools from quantum information theory to study several interesting problems in quantum field theory. The topics analysed range from the study of the Aharonov-Bohm effect in QFT using entanglement entropy, to the consistence of the Ryu-Takayanagi formula (proposed in the context of the AdS/CFT duality) using properties of relative entropy. We show that relative entropy can also be used to obtain new interesting quantum energy inequalities, that constrain the spatial distribution of negative energy density.

Noboru Watanabe, Andrei Yu. Khrennikov

Alexander Maloney, Jonathan J. Heckman, Vijay Balasubramanian

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. Our formulation quantifies the information lost under renormalization group flow from the UV to the IR and leads us to a quantification of fine-tuning. This formalism also leads us to a criterion for distinguishability of low energy effective field theories generated by the string theory landscape.

Noboru Watanabe