Real space entanglement in QFT and the Harvesting Protocol
Sergi Nadal-Gisbert, University of Valencia
507 (Pere Pascual)
Abstract: In QFT, even the simplest states within the simplest field theories, are highly entangled. This applies, in particular, to the vacuum of a non-interacting scalar theory in Minkowski spacetime. The main support for this statement comes from the calculation of entanglement entropy between a region of space and its complement. However, this involves considering a total pure state and infinitely many degrees of freedom. In this presentation I will introduce an operational approach to extract finite degrees of freedom from the field and quantify entanglement between them. The focus on finitely many modes of the field is motivated by the finite capabilities of real experiments. Our results show that entanglement between finite-dimensional subsystems is not common at all, and that one needs to carefully select the support of the modes for entanglement to show up.
Remarkably, when coupling a pair of Unruh-DeWitt detectors locally to the field and allowing them to interact over a certain duration, these detectors can extract entanglement from the vacuum state of the field, even when the pair of degrees of freedom to which the detectors are coupled remain unentangled. This phenomenon is known as Entanglement Harvesting. I will argue that this phenomenon arises from the fact that each detector explores a continuous family of modes from the field through time evolution and I will show that these two families of modes are indeed entangled.