Greenberger–Horne–Zeilinger Class State Research Articles

Analysing the Efficiencies of Partially Entangled Three-Qubit States for Quantum Information Processing Under Real Conditions

Abstract In this article, we revisit the question of analysing the efficiencies of partially entangled states in three-qubit classes under real conditions. Our results show some interesting observations regarding the efficiencies and correlations of partially entangled states. Surprisingly, we find that the efficiencies of many three-qubit partially entangled states exceed that of maximally entangled three-qubit states under real noisy conditions and applications of weak measurements. Our analysis, therefore, suggests that the efficiencies of partially entangled states are much more robust to noise than those of maximally entangled states at least for the GHZ (Greenberger–Horne–Zeilinger) class states, for certain protocols; i.e. less correlations in the initially prepared state may also lead to better efficiency and hence one need not always consider starting with a maximally entangled state with maximum correlations between the qubits. For a set of partially entangled states, we find that the efficiency is optimal, independent of the decoherence and state parameters, if the value of weak measurement parameter is very large. For other values of the weak measurement parameter, the robustness of the states depends on the decoherence and state parameters. Moreover, we further show that one can achieve higher efficiencies in a protocol by using non-optimal weak measurement strengths instead of optimal weak measurement strengths.

Efficient test to demonstrate genuine three particle nonlocality

According to the studies of genuine tripartite nonlocality in discrete variable quantum systems conducted so far, Svetlichny inequality is considered as the best Bell-type inequality to detect genuine (three way) nonlocality of pure tripartite genuine entangled states. In the present work, we have considered another Bell-type inequality (which has been reported as the 99th facet of NS2 local polytope in Bancal et al (2013 Phys. Rev. A 88 014102), to reveal genuine tripartite nonlocality of generalized GHZ (Greenberger–Horne–Zeilinger) class and a subclass of extended GHZ class states Acín et al (2000 Phys. Rev. Lett. 85 1560) thereby proving the conjecture given by Bancal et al (2013 Phys. Rev. A 88 014102) for the GGHZ class and the subclass of extended GHZ states. We compare the violation of this inequality with Svetlichny inequality which reveals the efficiency of the former inequality over the latter to demonstrate genuine nonlocality using the above classes of quantum states. Even in some cases discord monogamy score can be used as a better measure of quantum correlation over Svetlichny inequality for those classes of pure states. Besides, the 99th facet inequality is found efficient not only for revealing genuine nonlocal behavior of correlations emerging in systems using pure entangled states but also in some cases of mixed entangled states over Svetlichny inequality and some well known measures of entanglement.

Bell-type inequality and tripartite nonlocality in three-qubit GHZ-class states

In this paper, we theoretically study the relation between concurrence and nonlocality depicted by Bell-type inequality violation of quantum mechanics prediction versus local realism prediction for the GHZ (Greenberger -Horne-Zeilinger) class states. Analytical expressions of concurrence, violations of the Mermin inequality and the Svetlichny inequality are obtained. Through numerical calculations, the relationship between entanglement and nonlocality of GHZ-class states is discussed. Our results show that the concurrence is consistent with the degree of nonlocality described by violations of the two Bell-type inequalities of GHZ-class states. The Bell operator and its parameters can obviously reveal the nonlocal features of quantum states.

Scheme for Cloning a Three-Particle GHZ Class State with Assistance

Our concern is to design an assisted-clone scheme which can produce a perfect copy of a three-particle Greenberger—Horne—Zeilinger (GHZ) class state with a high probability. In the first stage of the protocol, the sender teleports the input state to the receiver by using three EPR pairs as the quantum channel. In the second stage of the protocol, a novel set of mutually orthogonal basis vectors is constructed. With the assistance of the preparer through a three-particle projective measurement under this basis, the perfect copy of an original state can be reestablished by the sender with the probability 1/2. Moreover, the classical communication cost of the scheme is also calculated.

Teleportation of unknown atomic entangled states via Greenberger–Horne–Zeilinger class states

A physical scheme for teleporting unknown atomic entangled states via three-atom non-maximally entangled states is proposed in cavity quantum electrodynamics. In this scheme, the Greenberger–Horne–Zeilinger class states are used as quantum channels. The most distinct feature of our scheme is that, not only the effects of the cavity decay and thermal field are eliminated, but also the teleportation and distillation procedure can be realized simultaneously.PACS Nos.: 03.67.Hk, 03.67.Pp

Remote Preparation of Three-Particle GHZ Class States

We propose a remote state preparation (RSP) scheme of three-particle Greenberger–Horne–Zeilinger (GHZ) class states, where quantum channels are composed of two maximally entangled states. With the aid of forward classical bits, the preparation of the original state can be successfully realized with the probability 1/2, the necessary classical communication cost is 0.5 bit on average. If the state to be prepared belongs to some special states, the success probability of preparation can achieve 1 after consuming one extra bit on average. We then generalize this scheme to the case that the quantum channels consist of two non-maximally entangled states.

Probabilistic remote preparation of a three-atom Greenberger–Horne–Zeilinger class state via cavity quantum electrodynamics

We present two schemes for remotely preparing a three-atom Greenberger–Horne–Zeilinger class state via entanglement swapping in cavity quantum electrodynamics. We show that each of our schemes can be achieved probabilistically by means of separate atomic measurements with the choice of an appropriate atom-cavity field interaction time.PACS Nos.: 03.67–a, 03.67.Lx, 42.50.Dv

Classical communication cost and remote preparation of the four-particle GHZ class state

We present a scheme for probabilistic remote preparation of the four-particle Greenberger–Horne–Zeilinger (GHZ) class state by using two partial entangled three-particle GHZ states as the quantum channel. The successful total probability and classical communication cost are calculated. Our results show that such remote state preparation requires only 1 bit classical communication cost for the maximally entangled channel.

Implementing remotely a single-qubit rotation operation by three-qubit entanglement

We investigate the problem of quantum remote implementation of a single-qubit rotation operation using three-qubit entangled state. Firstly, we utilize the entanglement property of maximally entangled Greenberger–Horne–Zeilinger (GHZ) state to design a theoretical scheme for implementing the operation remotely with unit fidelity and unit probability. Then, we put forward two schemes for conclusive implementing the non-local single-qubit rotation with unit fidelity by employing a partially entangled pure GHZ state as quantum channel. The features of these schemes are that a third side is included, who may participate the process of quantum remote implementation as a supervisor. Furthermore, when the quantum channel is partially entangled, the third side can rectify the state distorted by imperfect quantum channel. In addition to the GHZ class state, the W class state can also be used to remotely implement the same operation probabilistically. The probability of successful implementation using the W class state is always less than that using the GHZ class state.