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Register a new userCanonical operators and the optimal concentration of three-qubit Greenberger-Horne-Zeilinger states
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It is well known that quantum states that can be transformed into each other by local unitary transformations are equal from the information theoretic point of view. This defines equivalence classes of states and allows one to write any state with the minimal number of parameters called the canonical form of the state. We define the equivalence classes of local measurements such that local operations which transform states from one equivalence class into another with the same probability are equivalent. This equivalence relation allows one to write the operators with the minimal number of parameters, which we call canonical operators, and hence the use of the canonical operators simplifies the optimal manipulation of quantum states. We use the canonical local operators for the concentration of three-qubit Greenberger-Horne-Zeilinger states and obtain the optimal concentration protocols in terms of the unitary invariants of quantum states, namely, the bipartite concurrences and the three-tangle.
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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.
In this paper, we investigate the genuine three-way nonlocality which is recognized as the strongest form of tripartite correlations. We consider theoretically and experimentally a series of suitable Bell-type inequalities a violation of which is sufficient for the detection of three-way nonlocality. For the generalized GHZ (gGHZ) states, it is demonstrated that they do violate tripartite Bell-type inequalities for any degree of tripartite entanglement even if they do not violate Svetlichny inequality. It implies that three-way entangled gGHZ can always exhibit genuine three-way nonlocality under the requirement of time-order-dependent principle. Furthermore, we have determined the maximal amount of noise admissible for the gGHZ states to still remain genuine three-way nonlocal.
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 $N$-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.
Bells theorem shows a profound contradiction between local realism and quantum mechanics on the level of statistical predictions. It does not involve directly Einstein-Podolsky-Rosen (EPR) correlations. 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 twenty years ago, and followed by demonstrations for more qubits. Still, the GHZ contradictions underlying the tests can be reduced to three-qubit one. We show an irreducible four-qubit GHZ paradox, and report its experimental demonstration. The reducibility loophole is closed. The bound of a three-setting per party Bell-GHZ inequality is violated by $7sigma$. The fidelity of the GHZ state was around $81%$, and an entanglement witness reveals a violation of the separability threshold by $19sigma$.
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