Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation

TL;DR

This paper introduces a symmetry-based technique to significantly reduce computational complexity in evaluating quantum correlation bounds, making previously infeasible problems tractable in quantum information theory.

Contribution

The authors develop a symmetry exploitation method for semidefinite relaxations, enabling efficient computation of quantum correlation bounds in finite-dimensional systems.

Findings

Reduces computational requirements by several orders of magnitude.

Successfully certifies non-projectiveness of high-dimensional measurements.

Provides a user-friendly software package for broader application.

Abstract

We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The technique, which we make publicly available through a user-friendly software package, relies on the exploitation of symmetries present in the optimisation problem to reduce the number of variables and the block sizes in semidefinite relaxations. It is widely applicable in problems encountered in quantum information theory and enables computations that were previously too demanding. We demonstrate its advantages and general applicability in several physical problems. In particular, we use it to robustly certify the non-projectiveness of high-dimensional measurements in a black-box scenario based on self-tests of $d$-dimensional symmetric informationally complete POVMs.