A Spacetime Area Law Bound on Quantum Correlations

TL;DR

This paper proves a spacetime area law for quantum correlations in lattice systems, showing that correlations between measurement outcomes inside and outside a region are bounded by the region's spacetime boundary.

Contribution

It establishes a spacetime area law for quantum correlations in lattice systems, extending traditional area laws to spacetime regions under local quantum operations.

Findings

Quantum mutual information is bounded by the spacetime boundary area.

Spacetime correlations obey an area law in quantum lattice systems.

The result applies to sequences of local quantum operations over discrete times.

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.