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Journal of Optoelectronics·laser

Investigation of the robustness of four qubit hyper-entangled state

Zhao Jia-qian

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Using the methods of parametric down conversion and coherent superposition in composite beam splitter,four bits hyper-entangled Greenberger-Horne-Zeilinger states have been prepared.Contrast and fidelity of the entangled system have also been measured.Through the theoretical analysis of Ardehali inequality,we obtain a measurable Ardehali operator of the four qubit system.Using the relation between the expected value of Ardehali operator and the bit reversal noise intensity,the robustness of the four qubit system is investigated.The results show that the violation of Ardehali inequality versus local realism results decreases with the noise intensity increasing.

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Using the methods of parametric down conversion and coherent superposition in composite beam splitter,four bits hyper-entangled Greenberger-Horne-Zeilinger states have been prepared.Contrast and fidelity of the entangled system have also been measured.Through the theoretical analysis of Ardehali inequality,we obtain a measurable Ardehali operator of the four qubit system.Using the relation between the expected value of Ardehali operator and the bit reversal noise intensity,the robustness of the four qubit system is investigated.The results show that the violation of Ardehali inequality versus local realism results decreases with the noise intensity increasing.
By exploiting both the photons’ polarization and spatial degrees of freedom, we experimentally demonstrate a hyper-entangled four-photon six-qubit Greenberger-Horne-Zeilinger (GHZ) state. Based on the state, we experimentally test the multi-particle Ardehali inequality and prove the theoretical prediction of Ardehali. Furthermore, we experimentally first investigate the robustness of the Ardehali inequality for the four-photon six-qubit GHZ state in a bit-flip noise environment and show the good robustness against decoherence for this inequality. Our works provide an experimental benchmark to estimate the safety of quantum channel in the noisy environment.
The highest qubit Ardehali inequality violation with 203 standard deviations is first experimentally demonstrated using the hyper-entangled four-photon-eight-qubit Greenberger-Horne-Zeilinger (GHZ) state. Moreover, we experimentally investigate the robustness of the Ardehali inequality for the four-, six-, and eight-qubit GHZ states in a rotary noisy environment systematically. Our results first validate the Ardehali' theoretical statement of relation between violation of Ardehali inequality and particle number, and proved that Ardehali inequality is more robust against noise in larger number qubit GHZ states, and provided an experimental benchmark for us to estimate the safety of quantum channel in the noisy environment.
Knowing the level of entanglement robustness against quantum bit loss or decoherence mechanisms is an important issue for any application of quantum information. Fidelity of states can be used to judge whether there is entanglement in multi-particle systems. It is well known that quantum channel security in QKD can be estimated by measuring the robustness of Bell-type inequality against noise. We experimentally investigate a new Bell-type inequality (NBTI) in the three-photon Greenberger-Horne-Zeilinger (GHZ) states with different levels of spin-flip noise. The results show that the fidelity and the degree of violation of the NBTI decrease monotonically with the increase of noise intensity. They also provide a method to judge whether there is entanglement in three-particle mixed states.
Due to the important role of quantum information technology in the future development of science and technology, researchers have extensively studied the preparation, characterization, and application of quantum systems. It is of great significance to further study the universality and generalization of multi-qubit entangled states. Especially in quantum communication, the actual quantum system is always affected by various noises from the environment. Noise has a significant impact on the properties of the actual quantum system, so we study the effects of noise on a prepared two-photon four-qubit state by two methods. We experimentally simulated the most common bit-flip noise in quantum systems. The law of evolution of the fidelity of two-dimensional four-qubit states and violation of the Mermin inequality and the Ardehali inequality for LR under different levels of bit-flip noise are investigated. The experimental results show that entanglement fidelity and nonlocality can be used to judge the degree of noise interference in the quantum channel and, thus, judge the security of the quantum communication channel. This judgment is of great significance for the realization of practical long-distance multi-node quantum communication.
Ardehali (Phys. Rev. A, 46, 5375 (1992). 10.1103/PhysRevA.46.5375 ) derived a Bell-type inequality for an n-particle system in a Greenberger–Horne–Zeilinger (GHZ) state. This inequality helps relax the detection efficiencies required for closing the detection loophole in Bell tests. Coffman et al. (Phys. Rev. A, 61, 052306 (2000). doi: 10.1103/PhysRevA.61.052306 ) gave a simplified form of tripartite entanglement of three-qubit pure states. We use theory and experiment to investigate both results using three-qubit GHZ states with different intensities of bit-flip noise. The purpose of our work is to relate the Ardehali inequality and the tripartite concurrence of the tripartite GHZ states in a noisy environment. Our results show that the experimental values are quite consistent with theoretical predictions for three-qubit GHZ states in a bit-flip noisy environment.
There are different families of inequalities that can be used to characterize the entanglement of multiqubit entangled states by the violation of quantum mechanics prediction versus local realism prediction. In a noisy environment, the violation of different inequalities distinguishes a direct from a noise-free environment. That is, each inequality has a different robustness against noise. We investigate theoretically and experimentally this proposition with the Mermin inequality, Bell inequality, and Svetlichny inequality using three-qubit GHZ states for different levels of noise. Our purpose is to determine which one of the inequalities is more robust against noise and thus more suitable to characterize entanglement of states. Our results show that the Mermin inequality is the most robust against stronger noise and is, thus, more suitable for characterizing the entanglement of three-qubit GHZ states in a noisy environment.