Experimental detection of entanglement certainly disturbs the underlying shared state. It is possible that the entanglement content of the system is lost in the process of its detection. This observation has led to the study of sequential detection properties of various quantum correlations. Here, we investigate the sequential detection of genuinely multipartite entanglement of quantum systems composed of an arbitrary number of qubits. In order to detect genuine multipartite entanglement sequentially, observers can recycle any fixed subset of all the qubits, thus leading to a hierarchy of scenarios, categorized according to the number of qubits which are recycled by the observers. We show that the sequential detection of genuine multipartite entanglement, for every scenario in the hierarchy, leads to an unboundedly long sequence. This is shown to be possible if the initial state shared among the observers is the multipartite generalized Greenberger-Horne-Zeilinger state and is a class of mixed states. A comparison among different hierarchical scenarios is drawn based on the number of sequential detections of genuine multipartite entanglement for a specific measurement strategy employed by observers.
Experimental detection of entanglement certainly disturbs the underlying shared state. It is possible that the entanglement content of the system is lost in the process of its detection. This observation has led to the study of sequential detection properties of various quantum correlations. Here, we investigate the sequential detection of genuinely multipartite entanglement of quantum systems composed of an arbitrary number of qubits. In order to detect genuine multipartite entanglement sequentially, observers can recycle any fixed subset of all the qubits, thus leading to a hierarchy of scenarios, categorized according to the number of qubits which are recycled by the observers. We show that the sequential detection of genuine multipartite entanglement, for every scenario in the hierarchy, leads to an unboundedly long sequence. This is shown to be possible if the initial state shared among the observers is the multipartite generalized Greenberger-Horne-Zeilinger state and is a class of mixed states. A comparison among different hierarchical scenarios is drawn based on the number of sequential detections of genuine multipartite entanglement for a specific measurement strategy employed by observers.
We show that genuine multipartite entanglement of an arbitrary number of qubits can be witnessed sequentially for an arbitrary number of times. In the simplest scenario where only one qubit is subjected to sequential measurements, we show that genuine multiparty entanglement can be detected arbitrarily many times starting from generalized Greenberger-Horne-Zeilinger, cluster, graph, and a class of mixed states. For the case where multiple qubits are subjected to sequential measurements, we again show that detection of genuine multiparty entanglement is possible for an arbitrary number of times for multipartite Greenberger-Horne-Zeilinger and a class of mixed states.
We investigate the scenario where an observer, Alice, shares a two-qubit state with an arbitrary number of observers, Bobs, via sequentially and independently recycling the qubit in possession of the first Bob. It is known that there exist entangled states which can be used to have an arbitrarily long sequence of Bobs who can violate the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality with the single Alice. We show that there exist entangled states that do not violate the Bell inequality and whose entanglement can be detected by an arbitrary number of Bobs by suitably choosing the entanglement witness operator and the unsharp measurement settings by the Bobs. This proves that the set of states that can be used to witness entanglement sequentially is larger than those that can witness sequential violation of local realism. There exist, therefore, two-party quantum correlations that are Bell ``classical'', but whose entanglement ``nonclassicality'' can be witnessed sequentially and independently by an arbitrarily large number of observers at one end of the shared state with the single observer at the other end.
Two spatially separated observers, Alice and Bob, share a bipartite two-qubit entangled state and perform measurements to witness entanglement. After their measurements, they pass their qubits to a subsequent pair of observers who try to perform the same task independently, and so on. Here we ask: what is the maximum number of such pairs that can perform this task successfully? It has previously been conjectured that not more than one pair of observers can detect Clauser-Horne-Shimony-Holt ``Bell-nonlocal'' correlations in this setup. We prove that, on the contrary, entanglement can be witnessed by arbitrarily many pairs of observers. The dissimilar nature between entanglement and Bell-nonlocal correlations is therefore uncovered in a rather radical way, when considering sequentially acting pairs of observers. We prove this statement to be true when the initial shared state is any pure entangled state, a class of Bell-nonlocal mixed states, or a class of Bell-local entangled states.
Recently, Sasmal et al. [Phys. Rev. Lett. 133, 170201 (2024)] introduced probabilistic projective measurements (PPMs) for sequential sharing of nonlocality. Here we develop a general framework for sequentially witnessing quantum correlations, including bipartite and genuine multipartite entanglement, via PPMs. We show that a class of positive-operator-valued measures admits a unified PPM realization and present an explicit formula linking the initial state, intermediate channels, and witness operators, providing both computational efficiency and structural insight. Using this framework, we demonstrate unbounded sequential entanglement sharing for pure and certain mixed states, as well as detection of genuine multipartite entanglement in Greenberger-Horne-Zeilinger-type states. Our results highlight the nontrivial role of PPMs in sequential entanglement witnessing and address generalized multipartite sharing, as discussed in a recent review article [Phys. Rep. 1098, 1 (2025)].
We construct a set of criteria detecting genuine multipartite entanglement in arbitrary dimensional multipartite systems. These criteria are optimally suited for detecting multipartite entanglement in n-qubit Dicke states with m excitations, as shown in exemplary cases. Furthermore, they can be employed to detect multipartite entanglement in different states related to quantum cloning, decoherence-free communication, and quantum secret sharing. In a detailed analysis, we show that the criteria are also more robust to noise than any other criterion known so far, especially with increasing system size. Furthermore, it is shown that the number of required local observables scales only polynomially with size, thus making the criteria experimentally feasible.
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.