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Optics Express

Experimental violation of the local realism for four-qubit Dicke state

Yuanyuan Zhao, Yu-Chun Wu, Guo‐Yong Xiang, Chuan‐Feng Li, Guang‐Can Guo

Published Nov 13, 2015• 10 citations
Publisher

Abstract

Dicke state is an widely used type of multi-particle entangled state in quantum information. However, very few works have been done on its nonlocality. Here we prepare a four-photon symmetric Dicke state, whose fidelity is as high as 0.904 ± 0.004, and devise a simple Bell-type inequality to demonstrate that it violates the local realism with 12 standard deviation.

DOI
10.1364/oe.23.030491

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Dicke state is an widely used type of multi-particle entangled state in quantum information. However, very few works have been done on its nonlocality. Here we prepare a four-photon symmetric Dicke state, whose fidelity is as high as 0.904 ± 0.004, and devise a simple Bell-type inequality to demonstrate that it violates the local realism with 12 standard deviation.
We present an experimental and theoretical characterization of the sym- metric four-qubit entangled Dicke state with two excitations D (2) . We investigate the state's violation of local realism and study its characteristic properties with re- spect to quantum information applications. For the experimental observation of the state we used photons obtained from parametric down conversion. This allowed, in a simple experimental set-up, quantum state tomography yielding a fidelity as high as 0.844 ± 0.008.
The correlations between local measurement results are characteristic for multi-partite quantum systems. Under the condition of local realism, which assumes that properties of physical systems exist independent of being measured, and that space-like separated actions on the system cannot influence each other, these correlations are constrained by Bell-inequalities. Quantum mechanics predicts correlations which are not explainable under these two assumptions. The resulting violation of Bell inequalities was originally studied for pairs of entangled particles (Einstein et al.,1935). Meanwhile these ideas were extended to three-and more partite quantum states in particular with respect to the different kinds of multi-particle entanglement and their implications on the obtainable correlations (Mermin, 1990). Here we present a method to construct characteristic Bell inequalities for particular four-qubit states. These inequalities are a versatile tool, not only to provide evidence for non-locality, but also for the characterization of the states, with respect to detection of genuine multipartite entanglement and to state discrimination. Exemplarily we apply our approach to the symmetric four qubit Dicke-state (Dicke, 1954) with two excitations. (A symmetric N-qubit Dicke state with M excitations is the equal superposition of N-qubit pure product states having M logical 1 's and (N-M) logical 0's.) Experimentally the state was observed with photons as carrier of the qubits, using polarization encoding.
Cluster states are a new type of multiqubit entangled states with entanglement properties exceptionally well suited for quantum computation. In the present work, we experimentally demonstrate that correlations in a four-qubit linear cluster state cannot be described by local realism. This exploration is based on a recently derived Bell-type inequality [V. Scarani et al., Phys. Rev. A 71, 042325 (2005)] which is tailored, by using a combination of three- and four-particle correlations, to be maximally violated by cluster states but not violated at all by GHZ states. We observe a cluster-state Bell parameter of 2.59+/-0.08, which is more than 7sigma larger than the threshold of 2 imposed by local realism.
Violation of the Bell-type inequalities is necessary to confirm the existence of nonlocality in nonclassical (entangled) states. We have designed a customized operator which is made of the sum of the Pauli matrices (σxσ_xσx​, σyσ_yσy​, and σzσ_zσz​). We theoretically and experimentally investigate the violation of Bell-type inequalities using two- and four-qubit Dicke states on IBM Quantum Processing Units (QPUs). We compare two different state preparation methods for the four-qubit Dicke state -- gate-based and statevector-based -- and evaluate their performance on two IBM QPUs, \texttt{ibm\_kyiv} and \texttt{ibm\_sherbrook}. For the two-qubit case, we demonstrate clear violations of the CHSH inequality, with the highest observed Bell parameter reaching 2.821±0.00192.821 \pm 0.00192.821±0.0019 using M3 error mitigation, which is within 0.7σ0.7σ0.7σ of the theoretical maximum 222\sqrt{2}22​. In the four-qubit case, we employ a Bell-type inequality tailored for Dicke states and achieve a maximum violation of 2.607±0.0292.607 \pm 0.0292.607±0.029 without the need for additional mitigation when using the statevector-based method. Our results reveal that advanced error mitigation techniques significantly enhance the observed violations in the gate-based method, while the statevector-based approach inherently yields more robust states with lower noise. This study highlights the critical role of state preparation and mitigation techniques in probing fundamental quantum correlations on near-term quantum hardware.
We report the first experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the nonstatistical GHZ conflicts between quantum mechanics and local realism are confirmed, within the experimental accuracy, by four specific measurements of polarization correlations between four photons. In addition, our experimental results also demonstrate a strong violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations. Such a violation can only be attributed to genuine four-photon entanglement.