We establish the profound equivalence between the coherence measures defined via the convex roof method and two classes of genuine multipartite entanglement (GME) under certain conditions. Initially we construct two distinct classes of measures for genuine multipartite entanglement utilizing real symmetric concave functions and the convex roof technique. We then demonstrate that all coherence measures for any qudit states, defined through the convex roof approach, are identical to our two classes of GME measures of the states combined with an incoherent ancilla under an incoherent unitary operation. This relationship implies that genuine multipartite entanglement can be generated from the coherence incoherent in an initial state through the incoherent unitary operations. Furthermore, we conduct a preliminary exploration into the interplay between coherence and genuine quantum correlations such as genuine multipartite steering and genuine multipartite nonlocality. We show that the coherence exists in a qubit state if and only if genuine multipartite nonlocality is present for the special three-qubit
X states, obtained by performing unitary incoherent operations on the tensor product of the qubit state and the incoherent ancilla. Moreover, under the above process, we prove that the coherence of the qubit state exists if and only if the corresponding special
X state is genuinely multipartite steerable.
Abstract In the present paper, a novel framework to detect genuine multipartite entanglement (GME) has been presented by computing correlations in mutually unbiased bases (MUBs). It has been shown that correlation obtained by measuring in MUBs of all biseparable multipartite states satisfy a bound, whereas GME states violate it. Thus, the presented framework turns out to be a sufficient criterion to detect entanglement in a many-body scenario. The methodology paves a suitable way to demonstrate certification of different classes of tripartite and quadripartite GME states. In addition to its operational universality, correlation obtained by measuring in MUBs is shown to be juxtaposed with some well-known genuine tripartite and quadripartite entanglement measures.
We study genuine multipartite entanglement (GME) in a system of n qubits prepared in symmetric Dicke states and subjected to the influences of noise. We provide general, setup-independent expressions for experimentally favorable tools such as fidelity- and collective spin-based entanglement witnesses, as well as entangled-class discriminators and multi-point correlation functions. Besides highlighting the effects of the environment on large qubit registers, we also discuss strategies for the robust detection of GME. Our work provides techniques and results for the experimental communities interested in investigating and characterizing multipartite entangled states by introducing realistic milestones for setup design and associated predictions.