Genuine 3-qubit entanglement comes in two different inconvertible types represented by the Greenberger-Horne-Zeilinger (GHZ) state and the W state. We describe a specific method based on local positive operator valued measures and classical communication that can convert the ideal N-qubit GHZ state to a state arbitrarily close to the ideal N-qubit W state. We then experimentally implement this scheme in the 3-qubit case and characterize the input and the final state using 3-photon quantum state tomography.
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.
The concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is a new type of multipartite entangled state, which has potential application in future quantum information. In this paper, we propose a protocol of constructing arbitrary C-GHZ entangled state approximatively. Different from the previous protocols, each logic is encoded in the coherent state. This protocol is based on the linear optics, which is feasible in experimental technology. This protocol may be useful in quantum information based on the C-GHZ state.
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 study the generation of Greenberger-Horne-Zeilinger (GHZ) states of three path-encoded photons. Inspired by the seminal work of Bouwmeester et al. [1] on polarization-entangled GHZ states, we find a corresponding path representation for the photon states of an optical circuit, identify the elements required for the state generation, and propose a possible implementation of our strategy. Besides the practical advantage of employing an integrated system that can be fabricated with proven lithographic techniques, our example suggests that it is possible to enhance the generation efficiency by …
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 describe a novel method for producing Greenberger-Horne-Zeilinger states in cold atoms coupled to a superconducting coplanar cavity. In the proposed scheme, atoms interact between each other by virtual photon exchange via a cavity mode. These interactions cause an asymmetric Rydberg blockade mechanism that suppresses simultaneous excitations into different atomic Rydberg levels, thus forcing all atoms to occupy the same Rydberg state. This mechanism has effect even if the atoms are separated by distances of the order of millimeters. The atomic populations are transferred adiabatically from …
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…
We propose a scheme to generate Greenberger-Horne-Zeilinger (GHZ) state for N superconducting qubits in a circuit QED system. By sinusoidally modulating the qubit-qubit coupling, a synthetic magnetic field has been made which broken the time-reversal symmetry of the system. Directional rotation of qubit excitation can be realized in a three-qubit loop under the artificial magnetic field. Based on the special quality that the rotation of qubit excitation has different direction for single- and double-excitation loops, we can generate three-qubit GHZ state and extend this preparation method to a…
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…
Quantum squeezing and entanglement of spins can be used to improve the sensitivity in quantum metrology. Here we propose a scheme to create collective coupling of an ensemble of spins to mechanical vibrational mode actuated by an external magnetic field. We find an evolution time where the mechanical motion decouples from the spins, and the accumulated geometric phase yields a squeezing of $5.9~\text{dB}$ for $20$ spins. We also show the creation of a Greenberger-Horne-Zeilinger spin state for $20$ spins with a fidelity of $\sim 0.62$ at cryogenic temperature. The numerical simulations show th…
The concatenated Greenberger-Horne-Zeiglinger (C-GHZ) state which is a new type of logic-qubit entanglement has attracted a lot of attentions recently. We present a feasible entanglement concentration protocol (ECP) for logic-qubit entanglement. This ECP is based on the linear optics, and it does not know the initial coefficients of the less-entangled C-GHZ state. This protocol can be extended to arbitrary C-GHZ state. This protocol may be useful in future quantum information processing tasks.
A quantitative witness for Greenberger-Horne-Zeilinger entanglement
随着实验量子技术的巨大进步，对三个或更多量子系统之间纠缠的量化需求越来越大。理论仍然没有为此目的提供足够的工具。我们的目标是，除了寻求准确的结果，开发操作方法，允许有效的纠缠量化。在这里，我们提出了一个分析方法，服务于这两个目标。我们提供了一个简单的方法来量化任意三比特态的Greenberger-Horne-Zeilinger型多体纠缠。对于两个量子位，该方法相当于Wootters的开创性结果[Phys. Rev. Lett. 80，2245（1998）]。它建立了纠缠量化和纠缠检测证人之间的密切联系，并可以推广到更高的维度和超过三方。
