Indirect Quantum Tomography of Quadratic Hamiltonians

TL;DR

This paper introduces an efficient indirect method for estimating quadratic Hamiltonians in many-body quantum systems, enabling property measurement even from mixed states with minimal resources.

Contribution

It presents a novel approach to quantum Hamiltonian estimation that relies on surface properties and is applicable to diverse physical models.

Findings

Properties of quadratic Hamiltonians are determined by their surface.

The method works with systems initialized in mixed states.

Efficient estimation requires very few resources.

Abstract

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We find that almost all properties of the Hamiltonian are determined by its surface, and that these properties can be measured even if the system can only be initialised to a mixed state. Therefore our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices, and transverse Ising chains.