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 scenario is that where one aims at determining all the reduced states up to a given size. This is achieved by overlapping tomography, which we review here; it makes strong use of parallelization 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. We introduce local overlapping tomography, aimed at that case (arXiv:2112.03924). First of all, we show that, contrary to its full version, the number of product measurements needed for local overlapping tomography does not grow with system size. Then, we present strategies for qubit and fermionic systems based on graph-coloring results, and also examples in selected lattice geometries.

Finally, we present perspectives for further work on the question of when overlapping tomography is (almost) sufficient for full state description.

A sala estará aberta a partir das 15H15.

Grupo de Óptica e Informação Quântica
Instituto de Física – UFRJ