Abstract
Entanglement is a fascinating feature, typical and ubiquitous to the science of quantum information and computation. Over the last few decades, we have seen entanglement, or more precisely bipartite entanglement, playing an unparalleled role in various quantum information-theoretic tasks [1–3]. Multipartite entanglement comes with an even richer structure and a whole new set of features providing information processing advantages in quantum communication, simulation, or metrology. It is therefore essential to construct methods to identify genuinely multipartite entangled states [4–6]. However, detecting entanglement of an arbitrary quantum state is a problem of significant complexity [7, 8]. Thus, witnessing entanglement by using versatile experimentally feasible tools [9–18] is a challenging task. In the case of multipartite entanglement, the challenge enhances significantly and demands greater interest from the scientific community. In this paper, we propose a protocol to detect multipartite entanglement by utilizing the well-known phenomenon of non-Markovianity in open quantum systems [19, 20] and the theory of positive maps. The positive maps that are not completely positive can detect bipartite entanglement quite effectively, Partial Transposition [21] being a well-known example. Unfortunately, this technique cannot be directly extended to the case of multipartite entanglement, where diverse separability structures complicate the detection problem. Although semi-definite programming can be used to construct witnesses to certify genuine multipartite entangle