The $N$-qubit Greenberger-Horne-Zeilinger (GHZ) states are the maximally entangled states of $N$ qubits, which have had many important applications in quantum information processing, such as quantum key distribution and quantum secret sharing. Thus how to distinguish the GHZ states from other quantum states becomes a significant problem. In this work, by presenting a family of the generalized Clauser-Horne-Shimony-Holt (CHSH) inequality, we show that the $N$-qubit GHZ states can be indeed identified by the maximal violations of the generalized CHSH inequality under some specific measurement settings. The generalized CHSH inequality is simple and contains only four correlation functions for any $N$-qubit system, thus has the merit of facilitating experimental verification. Furthermore, we present a quantum phenomenon of robust violations of the generalized CHSH inequality, in which the maximal violation of Bell's inequality can be robust under some specific noises adding to the $N$-qubit GHZ states.
A general argument is presented against relativistic, unitary, single-outcome quantum mechanics. This is achieved by combining the Wigner's Friend thought experiment with measurements on a Greenberger-Horne-Zeilinger (GHZ) state, and describing the evolution of the quantum state in various inertial frames. Assuming unitary quantum mechanics and single outcomes, the result is that the Born rule must be violated in some inertial frame: in that frame, outcomes are obtained for which no corresponding term exists in the pre-measurement wavefunction.
The Greenberger-Horne-Zeilinger (GHZ) argument against noncontextual local hidden variables is recast in quantum logical terms of fundamental propositions, states and probabilities. Unlike Kochen-Specker- and Hardy-like configurations, this operator based argument proceeds within four nonintertwining contexts. The nonclassical performance of the GHZ argument is due to the choice or filtering of observables with respect to a particular state. We study the varieties of GHZ games one could play in these four contexts, depending on the chosen state of the GHZ basis.
A protocol for generating Greenberger-Horne-Zeilinger states in a system of $N$ coupled qubits is proposed. The Hamiltonian model assumes $N$-wise interactions between the $N$ qubits and the presence of a controllable time-dependent field acting upon one spin only. Implementing such a scenario is in the experimental reach. The dynamical problem is exactly solved thanks to the symmetries of the Hamiltonian model. The possibility of generating GHZ states under both adiabatic and non-adiabatic conditions is shown and discussed in detail.
We construct GHZ contradictions for three or more parties sharing an entangled state, the dimension d of each subsystem being an even integer greater than 2. The simplest example that goes beyond the standard GHZ paradox (three qubits) involves five ququats (d=4). We then examine the criteria a GHZ paradox must satisfy in order to be genuinely M-partite and d-dimensional.
We introduce a class of two-level multi-particle Greenberger-Horne-Zeilinger (GHZ) states, and study entanglement swapping between two systems for Bell states and the class of GHZ states in qubit systems, respectively. We give the formulas for the entanglement swapping of Bell states and GHZ states in any number of qubit systems. We further consider entanglement swapping between any number of Bell states and between any number of the introduced GHZ states, and propose a series of entanglement swapping schemes in a detailed way. We illustrate the applications of such schemes in quantum informat…
With a two step optimization method of entanglement witness, we analytically propose a set of necessary and sufficient entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger (GHZ) diagonal states. The criterion set contains four criteria. Two of them are linear with density matrix elements. The other two criteria are nonlinear with density matrix elements. The criterion set has a nest structure. A proper subset of the criteria is necessary and sufficient for the entanglement of a proper subset of the states. We illustrate the nest structure of criterion set with the general…
We propose a scheme to probabilistically generate Greenberger-Horne-Zeilinger (GHZ) states encoded on the path degree of freedom of three photons. These photons are totally independent from each other, having no direct interaction during the whole evolution of the protocol, which remarkably requires only linear optical devices to work, and two extra ancillary photons to mediate the correlation. The efficacy of the method, which has potential application in distribited quantum computation and multiparty quantum communication, is analyzed in comparison with similar proposals reported in the rece…
