# Reconstructing quantum states from single-party information

## TL;DR

This paper explores how local spectral information constrains the global quantum state, demonstrating stability of these constraints and applying them to fermionic systems to estimate correlation energy from single-particle data.

## Contribution

It proves the stability of quantum marginal constraints and applies this to fermionic systems to estimate correlation energy using only one-particle information.

## Key findings

- Global quantum state structure is stable under near-saturation of local spectral constraints.
- The method allows estimation of correlation energy loss from single-particle data.
- Application to fermionic systems extends Hartree-Fock accuracy assessment.

## Abstract

The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a specific, simplified structure. We prove that these remarkable global implications of extremal local information are stable, i.e. they hold approximately for spectra close to the boundary of the allowed region. Application of this general result to fermionic quantum systems allows us to characterize natural extensions of the Hartree-Fock ansatz and to quantify their accuracy by resorting to one-particle information, only: The fraction of the correlation energy not recovered by such an ansatz can be estimated from above by a simple geometric quantity in the occupation number picture.