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. arXiv:1807.09187v1 [quant-ph]

Path Integrals from Spacetime Quantum Actions

“…The possibility to extend the conventional framework of QM to remove the previous limitations has recently attracted renewed attention [3,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Not only due to its deep fundamental implications, closely related to the quantization of gravity [22][23][24][25] and the emergence of spacetime [26][27][28], but also because of the incentives and insights which follow from quantum information theory, where the conventional canonical formulation is mostly well suited, but e.g.…”