Generic construction of multipartite entanglement measures

Quantum physics is widely recognized as the most successful but counterintuitive physical theory. It has enabled significant technological advancements across diverse fields by providing incredibly accurate predictions about the behavior of microscopic particles. However, despite its success, many quantum phenomena are still beyond our classical intuition. Since the 1980s, the scientific community has undergone a paradigm shift in the way they study quantum phenomena. Instead of treating them as inexplicable conundrums, they are now viewed as useful resources. This shift led to the emergence of quantum information science, which explores the advantages that quantum theory can offer in processing and transferring information. It is now a well-established fact that encoding bits in quantum particles can lead to more efficient computations and extremely secure communications. One of the most useful and still fascinating features of quantum physics is entanglement. It occurs when a quantum state of two or more particles becomes correlated in such a way that the states of the individual particles cannot be described independently; instead, the overall system must be described as a whole. Entanglement is used as a quantum resource for tasks that can not be performed by classical resources. It can be manipulated, broadcast, controlled, and distributed. For this reason, it is important to somehow measure the amount of entanglement present in a certain system. This thesis aims to find a suitable measure to quantify genuine entanglement in multipartite systems, suitable in the sense that it has to satisfy certain properties to be valid. I propose a generic construction of multipartite entanglement measures. The genuine k-partite entanglement of a state represents how this state differs from the one that can be constructed through LOCC by the N laboratories when these are divided into subsets of at most k laboratories: it is within these subsets that the state is formed beyond the limitations imposed by LOCC. My measure takes into account this difference by considering the sum of bipartite entanglement between each of the particles of the subsets. In this construction, we solely use a generic bipartite entanglement measure. Thus, by construction, the proposed measure of genuine multipartite entanglement satisfies the desiderata properties of an entanglement measure. It also offers insights into the entanglement structure of an N partite quantum system across different producible partitions.