Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian

TL;DR

This paper introduces a method to generate highly entangled 2D quantum states with tunable entanglement properties using a correspondence with stochastic processes, and discusses their local parent Hamiltonians.

Contribution

It presents a novel approach linking stochastic processes to quantum state generation and provides a sequential protocol for creating complex entangled states with local Hamiltonians.

Findings

States with tunable entanglement structures (area, sub-volume, volume law)

Sequential generation protocol for these states

Conditions for local, frustration-free parent Hamiltonians

Abstract

We construct examples of highly entangled two-dimensional states by exploiting a correspondence between stochastic processes in $d$ dimensions and quantum states in $d+1$ dimensions. The entanglement structure of these states, which we explicitly calculate, can be tuned between area law, sub-volume law, and volume law. This correspondence also enables a sequential generation protocol: the states can be prepared through a series of unitary transformations acting on an auxiliary system. We also discuss the conditions under which these states have local, frustration-free parent Hamiltonians.