Local quantum overlapping tomography

TL;DR

This paper introduces a local overlapping tomography method that efficiently estimates reduced states of neighboring particles in many-body quantum systems, with measurement settings independent of system size, aiding quantum simulation and computing.

Contribution

It demonstrates that local overlapping tomography requires a fixed number of measurements regardless of system size and provides strategies for qubit and fermionic systems in lattice geometries.

Findings

Number of measurements for local tomography does not grow with system size.

Strategies developed for qubit and fermionic systems in lattice geometries.

Applicable to current quantum simulators with local interactions.

Abstract

Reconstructing the full quantum state of a many-body system requires the estimation of a number of parameters that grows exponentially with system size. Nevertheless, there are situations in which one is only interested in a subset of these parameters and a full reconstruction is not needed. A paradigmatic example is a scenario where one aims at determining all the reduced states only up to a given size. Overlapping tomography provides constructions to address this problem with a number of product measurements much smaller than what is obtained when performing independent tomography of each reduced state. There are however many relevant physical systems with a natural notion of locality where one is mostly interested in the reduced states of neighboring particles. In this work, we study this form of local overlapping tomography. First of all, we show that, contrary to its full version, the number of product-measurement settings needed for local overlapping tomography does not grow with system size. Then, we present strategies for qubit and fermionic systems in selected lattice geometries. The developed methods find a natural application in the estimation of many-body systems prepared in current quantum simulators or quantum computing devices, where interactions are often local.