# Entanglement Detection Via Frank-Wolfe Algorithms ongoing

We will apply a Frank-Wolfe-based approach for separability certification and entanglement detection of multipartite quantum states. The method will be further exploited to derive entanglement witnesses in the case, often encountered in experiments, of incomplete characterisation of the quantum state.

## đź§‘â€ŤđźŽ“ Project Members

## đźŞ™ Funding

This project is being funded by the Berlin Mathematics Research Center MATH+ (project ID AA2-19), itself funded by the German Research Foundation (DFG) under Germany's Excellence Strategy (EXC-2046/1, project ID 390685689) from January 2024 to December 2025.

## đź”¬ Project Description

Entanglement, a fundamental concept in quantum mechanics, lies at the heart of many quantum technologies and has captured the attention of scientists and researchers worldwide. The phenomenon of entanglement occurs when two or more quantum particles become intrinsically correlated, such that the state of one particle cannot be described independently of the others. This peculiar feature, famously referred to as ``spooky action at a distanceâ€™â€™ by Einstein, has perplexed and fascinated physicists since its discovery. Over the years, entanglement has emerged as a powerful resource for numerous applications, including quantum communication, quantum computing, and quantum sensing.

Detecting entanglement is a crucial step in harnessing its potential for quantum technologies. Several standard methods have been developed to ascertain the presence of entanglement in quantum systems. One such approach is the measurement of entanglement witnesses, which are observables that can discern entangled states from *separable* (or *disentangled*) ones. Mathematically, they consist of hyperplanes separating a specific state (in practice, dictated by the experimental setup) from the convex set of separable states.

Conditional gradient methods have seen success in quantum entanglement by producing certificates that a state is separable. The original Frank-Wolfe algorithm was rediscovered and suscitated a lot of interest, but the current applications in this domain suffer the same limitations as this original algorithm, upon which a lot of theoretical and applied progress has been made in the last decade. We thus expect significant improvements over existing methods, leading both to novel theoretical results in entanglement theory and immediate usage by experimental groups.

Currently, we utilize the the blended pairwise conditional gradient algorithm to achieve more accurate and robust separable bounds for the bound entanglement, which is very close to separable space and so hard to detect.