A Spacetime Area Law Bound on Quantum Correlations
Abstract
Area laws are a far-reaching consequence of the locality of physical interactions, and they are relevant in a range of systems, from black holes to quantum many-body systems. Typically, these laws concern the entanglement entropy or the quantum mutual information of a subsystem at a single time. However, when considering information propagating in spacetime, while carried by a physical system with local interactions, it is intuitive to expect area laws to hold for spacetime regions; in this work, we prove such a law in the case of quantum lattice systems. We consider a sequence of local quantum operations performed at discrete times on a spin-lattice, such that each operation is associated to a point in spacetime. In the time between operations, the time evolution of the spins is governed by a finite range Hamiltonian. By considering a purification of the quantum instruments and analyzing the quantum mutual information between the ancillas used in the purification, we obtain a spacetime area law bound for the correlations between the measurement outcomes inside a spacetime region, and those outside of it.
Cite
@article{arxiv.1807.09187,
title = {A Spacetime Area Law Bound on Quantum Correlations},
author = {Ilya Kull and Philippe Allard Guérin and Časlav Brukner},
journal= {arXiv preprint arXiv:1807.09187},
year = {2019}
}