Abstract The Greenberger–Horne–Zeilinger (GHZ) paradox shows that it is possible to create a multipartite state involving three or more particles in which the measurement outcomes of the particles are correlated in a way that cannot be explained by classical physics. We extend it to witness quantum networks. We first extend the GHZ paradox to simultaneously verify the GHZ state and Einstein–Podolsky–Rosen states on triangle networks. We then extend the GHZ paradox to witness the entanglement of chain networks consisting of multiple GHZ states. All the present results are robust against the noise.
Abstract The Greenberger–Horne–Zeilinger (GHZ) paradox shows that it is possible to create a multipartite state involving three or more particles in which the measurement outcomes of the particles are correlated in a way that cannot be explained by classical physics. We extend it to witness quantum networks. We first extend the GHZ paradox to simultaneously verify the GHZ state and Einstein–Podolsky–Rosen states on triangle networks. We then extend the GHZ paradox to witness the entanglement of chain networks consisting of multiple GHZ states. All the present results are robust against the noise.
Future quantum information networks will consist of quantum and classical agents, who have the ability to communicate in a variety of ways with trusted and untrusted parties and securely delegate computational tasks to untrusted large-scale quantum computing servers. Multipartite quantum entanglement is a fundamental resource for such a network and, hence, it is imperative to study the possibility of verifying a multipartite entanglement source in a way that is efficient and provides strong guarantees even in the presence of multiple dishonest parties. In this Letter, we show how an agent of a quantum network can perform a distributed verification of a source creating multipartite Greenberger-Horne-Zeilinger (GHZ) states with minimal resources, which is, nevertheless, resistant against any number of dishonest parties. Moreover, we provide a tight tradeoff between the level of security and the distance between the state produced by the source and the ideal GHZ state. Last, by adding the resource of a trusted common random source, we can further provide security guarantees for all honest parties in the quantum network simultaneously.
The Greenberger-Horne-Zeilinger version of the Einstein-Podolsky-Rosen (EPR) paradox is widely regarded as a conclusive logical argument that rules out the possibility of reproducing the predictions of Quantum Mechanics within the framework of any physical theory sharing the notions of reality and relativistic causality that we acknowledge as a given in our classical descriptions of the macroscopic world. Thus, this renowned argument stands as a seemingly insurmountable roadblock on the path to a very desired, physically intuitive understanding of quantum phenomena and, in particular, quantum entanglement. In this paper, we notice, however, that the GHZ argument involves unaccounted spurious gauge degrees of freedom and that it can be overcome once these degrees are properly taken into account. It is then possible to explicitly build a successful statistical model for the GHZ experiment based on the usual notions of relativistic causality and physical reality. This model, thus, completes—in the EPR sense—the quantum description of the GHZ state and paves the way to a novel intuitive interpretation of the quantum formalism and a deeper understanding of the physical reality that it describes.
The paradox of Greenberger-Horne-Zeilinger (GHZ) disproves directly the concept of EPR elements of reality, based on the EPR correlations, in an all-versus-nothing way. A three-qubit experimental demonstration of the GHZ paradox was achieved nearly 20 years ago, followed by demonstrations for more qubits. Still, the GHZ contradictions underlying the tests can be reduced to a three-qubit one. We show an irreducible four-qubit GHZ paradox, and report its experimental demonstration. The bound of a three-setting-per-party Bell-GHZ inequality is violated by $7\ensuremath{\sigma}$. The fidelity of the GHZ state was around 81, and an entanglement witness reveals a violation of the separability threshold by $19\ensuremath{\sigma}$.
The Greenberger-Horne-Zeilinger (GHZ) version of the Einstein-Podolsky-Rosen (EPR) paradox is widely regarded as a conclusive logical argument that rules out the possibility of describing quantum phenomena within the framework of any model of local hidden variables in which the observers are free to choose their own experimental settings. In this paper, we show, however, that the GHZ argument implicitly relies on a subtle, though crucial, assumption that is not required by fundamental physical principles, and which had gone unnoticed. Namely, we note that the argument implicitly assumes the existence of an absolute angular frame of reference with respect to which the polarization properties of the hypothetical hidden configurations of the entangled particles, as well as the orientations of the measurement devices that test them, can be defined. We further note that such an absolute frame of reference may not exist if the hidden configurations of the entangled particles spontaneously break the gauge rotational symmetry. Indeed, by skipping the disputed requirement we are able to build a model of local hidden variables for the GHZ state, which complies with the 'free-will' hypothesis and reproduces the quantum mechanical predictions. Our model, thus, completes-in the EPR sense-the quantum description of the GHZ state.
Characterizing entanglement of systems composed of multiple particles is a very complex problem that is attracting increasing attention across different disciplines related to quantum physics. The task becomes even more complex when the particles have many accessible levels, i.e., they are of high dimension, which leads to a potentially high-dimensional multipartite entangled state. These are important resources for an ever-increasing number of tasks, especially when a network of parties needs to share highly entangled states, e.g., for communicating more efficiently and securely. For these applications, as well as for purely theoretical arguments, it is important to be able to certify both the high-dimensional and the genuine multipartite nature of entangled states, possibly based on simple measurements. Here we derive a novel method that achieves this and improves over typical entanglement witnesses like the fidelity with respect to states of a Greenberger-Horne-Zeilinger (GHZ) form, without needing more complex measurements. We test our condition on paradigmatic classes of high-dimensional multipartite entangled states like imperfect GHZ states with random noise, as well as on purely randomly chosen ones and find that, in comparison with other available criteria our method provides a significant advantage and is often also simpler to evaluate.
This work proposes an extended Mermin inequality based on a hybrid classical model that involves only one classical source, with the remaining sources being post-quantum. In a chain-structured quantum network consisting of hybrid Einstein–Podolsky–Rosen (EPR) pairs and Greenberger–Horne–Zeilinger (GHZ) states, joint measurements are performed at the central node, while local measurements are conducted at the peripheral nodes. This setup shows that the obtained quantum correlations can violate the proposed inequality with fewer measurement settings, thereby verifying network nonlocality. Furthermore, we extend this method to chain networks of arbitrary length n and show that the proposed inequality remains effective in verifying network nonlocality.