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Register a new userLocal Conversion of Greenberger-Horne-Zeilinger States to Approximate W States
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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.
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In device-independent quantum information processing Bell inequalities are not only used as detectors of nonlocality, but also as certificates of relevant quantum properties. In order for these certificates to work, one very often needs Bell inequalities that are maximally violated by specific quantum states. Recently, in [A. Salavrakos et al., Phys. Rev. Lett. 119, 040402 (2017)] a general class of Bell inequalities, with arbitrary numbers of measurements and outcomes, has been designed, which are maximally violated by the maximally entangled states of two quantum systems of arbitrary dimension. In this work, we generalize these results to the multipartite scenario and obtain a general class of Bell inequalities maximally violated by the Greenberger-Horne-Zeilinger states of any number of parties and any local dimension. We then derive analytically their maximal quantum and nonsignaling values. We also obtain analytically the bound for detecting genuine nonlocality and compute the fully local bound for a few exemplary cases. Moreover, we consider the question of adapting this class of inequalities to partially entangled GHZ-like states for some special cases of low dimension and small number of parties. Through numerical methods, we find classes of inequalities maximally violated by these partially entangled states.
We propose a probabilistic quantum cloning scheme using Greenberger-Horne-Zeilinger states, Bell basis measurements, single-qubit unitary operations and generalized measurements, all of which are within the reach of current technology. Compared to another possible scheme via Tele-CNOT gate [D. Gottesman and I. L. Chuang, Nature 402, 390 (1999)], the present scheme may be used in experiment to clone the states of one particle to those of two different particles with higher probability and less GHZ resources.
The hierarchy of nonlocality and entanglement in multipartite systems is one of the fundamental problems in quantum physics. Existing studies on this topic to date were limited to the entanglement classification according to the numbers of particles enrolled. Equivalence under stochastic local operations and classical communication provides a more detailed classification, e. g. the genuine three-qubit entanglement being divided into W and GHZ classes. We construct two families of local models for the three-qubit Greenberger-Horne-Zeilinger (GHZ)-symmetric states, whose entanglement classes have a complete description. The key technology of construction the local models in this work is the GHZ symmetrization on tripartite extensions of the optimal local-hidden-state models for Bell diagonal states. Our models show that entanglement and nonlocality are inequivalent for all the entanglement classes (biseparable, W, and GHZ) in three-qubit systems.
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 Bells inequality can be robust under some specific noises adding to the $N$-qubit GHZ states.
We introduce a class of multi-particle Greenberger-Horne-Zeilinger (GHZ) states, and study entanglement swapping between two qubit systems for Bell states and for the class of GHZ states, respectively. We generalize the bi-system entanglement swapping of Bell states and multi-particle GHZ states to any number of qubit systems. We further study the entanglement swapping schemes between any number of Bell states and between any number of the introduced GHZ states in a detailed way, and propose the schemes that can generate two identical GHZ states. We illustrate the applications of such schemes in quantum information processing by proposing quantum protocols for quantum key distribution, quantum secret sharing and quantum private comparison.
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