A spacetime area law bound on quantum correlations

Author(s)
Ilya Kull, Philippe Allard Guerin, Caslav Brukner
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 for quantum lattice systems. We consider two agents interacting in disjoint spacetime regions with a spin-lattice system that evolves in time according to a local Hamiltonian. In theft respective spacetime regions, the two agents apply quantum instruments to the spins. By considering a purification of the quantum instruments, and analyzing the quantum mutual information between the ancillas used to implement them, we obtain a spacetime area law bound on the amount of correlation between the agents' measurement outcomes. Furthermore, this bound applies both to signaling correlations between the choice of operations on the side of one agent, and the measurement outcomes on the side of the other; as well as to the entanglement they can harvest from the spins by coupling detectors to them.

Organisation(s)
Quantum Optics, Quantum Nanophysics and Quantum Information
External organisation(s)
Österreichische Akademie der Wissenschaften (ÖAW)
Journal
npj Quantum Information
Volume
5
No. of pages
5
ISSN
2056-6387
DOI
https://doi.org/10.1038/s41534-019-0171-x
Publication date
07-2019
Peer reviewed
Yes
Austrian Fields of Science 2012
103025 Quantum mechanics
Keywords
Portal url
https://ucris.univie.ac.at/portal/en/publications/a-spacetime-area-law-bound-on-quantum-correlations(ded0a469-a036-4ca0-8d00-e4565dfc9aca).html