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arXiv:1103.5107 · Physical Review A

Testing tripartite Mermin inequalities by spectral joint measurements of qubits

J. S. Huang, C. H. Oh, L. F. Wei

Published Jun 13, 2011• 10 citations
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Abstract

Using spectral joint measurements of the qubits, we propose a scheme to test the tripartite Mermin inequality with three qubits dispersively coupled to a driven cavity. First, we show how to generate a three-qubit Greenberger-Horne-Zeilinger (GHZ) state by only one-step quantum operation. Then spectral joint measurements are introduced to directly confirm such tripartite entanglement. Assisted by a series of single-qubit operations, these measurements are further utilized to test the Mermin inequality. The feasibility of the proposal is robustly demonstrated by the present numerical experiments.

DOI
10.1103/physreva.83.062108

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Canadian Journal of Physics•Jun 4, 2018•3 citations
Using spectral joint measurements of the qubits, we propose a scheme to test the tripartite Mermin inequality with three qubits dispersively coupled to a driven cavity. First, we show how to generate a three-qubit Greenberger-Horne-Zeilinger (GHZ) state by only one-step quantum operation. Then spectral joint measurements are introduced to directly confirm such tripartite entanglement. Assisted by a series of single-qubit operations, these measurements are further utilized to test the Mermin inequality. The feasibility of the proposal is robustly demonstrated by the present numerical experiments.
We propose a feasible approach to test quantum nonlocality with two qubits dispersively coupled to a driven cavity. Our proposal is based on spectral joint measurements of two qubits, i.e. , their quantum states in the computational basis states {| kl 〉, k , l = 0,1} can be measured nondestructively by detecting the steady-state transmission spectra of the driven cavity. With this kind of measurements, the existence of Bell state can be robustly confirmed instead of conventional quantum state tomography. Then this kind of measurements is further utilized to test CHSH-Bell inequality. The advantage and feasibility of our proposal are also discussed.
It is known that the violation of Svetlichny's inequality (SI), rather than the usual Mermin's inequality (MI), is a robust criterion to confirm the existence of genuine multipartite quantum nonlocality. In this paper, we propose a feasible approach to test SI with three two-level atoms (TLAs) dispersively coupled to a driven cavity. The proposal is based on the joint measurements of the states of three TLAs by probing the steady-state transmission spectra of the driven cavity: each peak marks one of the computational basis states and its relative height corresponds to the probability superposed in the detected three-TLA state. With these kinds of joint measurements, the correlation functions in SI can be directly calculated, and thus the SI can be efficiently tested for typical tripartite entanglement, i.e., genuine tripartite entanglement [e.g., Greenberger-Horne-Zeilinger (GHZ) and W states] and biseparable three-qubit entangled states (e.g., ${|\ensuremath{\chi}\ensuremath{\rangle}}_{12}{|\ensuremath{\xi}\ensuremath{\rangle}}_{3}$). Our numerical experiments show that the SI is violated only by three-qubit GHZ and W states, not by biseparable three-qubit entangled state ${|\ensuremath{\chi}\ensuremath{\rangle}}_{12}{|\ensuremath{\xi}\ensuremath{\rangle}}_{3}$, while the MI can still be violated by biseparable three-qubit entangled states. Thus the violation of SI can be regarded as a robust criterion for the existence of genuine tripartite entanglement.
Distributed entanglement across multi-node quantum networks is essential for a wide range of quantum technologies, including modular quantum computers, distributed sensing and metrology, and multi-party secure communication protocols. Such large-scale quantum networks will require photonic interconnects to generate and sustain entangled states across localized nodes. Previously, three-node distributed Greenberger-Horne-Zeilinger (GHZ) states have been generated between solid-state qubits and atomic ensembles, but not yet in the platform of individual atomic qubits, which can be replicated, detected, and individually controlled with high fidelity. Here we report the first fully-distributed GHZ state of qubits across a three-node quantum network of single atomic memories, using photonic interconnects. We achieve a bounded fidelity of 0.841(17)≤F≤0.881(17)0.841(17) \leq \mathcal{F} \leq 0.881(17)0.841(17)≤F≤0.881(17) at an entanglement generation rate of 0.095(5)/sec and measure a clear violation of Mermin's inequality while closing the detection loophole for the first time in a fully-distributed multipartite entangled state.
ABSTRACT Mermin's inequality provides a fundamental test to verify the quantum nonlocality of multipartite Greenberger–Horne–Zeilinger (GHZ) states, by also serving as a key resource for measurement‐based quantum computing. While the theoretical foundation of Mermin's inequality test is well established for both qubit and qudit systems, the experimental validation for qudits remains elusive. In this work, we perform qudit Mermin's inequality test implemented on a qutrit (i.e., three‐level system) GHZ state, where the multipartition is achieved by deterministically entangling the time and frequency bins of a biphoton state via standard fiber‐optic components. The direct measurement of Mermin's operator yields an expectation value of 8.612(44), surpassing the bound of 6 for local realism by 59 standard deviations. We demonstrate the potential of the verified GHZ state for high‐dimensional quantum computing by utilizing the nonlocality results to compute a ternary logic function through non‐adaptive high‐dimensional measurement‐based quantum computation. Our scheme is readily scalable to higher dimensions without additional loss or modifications to the experimental setup.
We propose a feasible approach to test Bell's inequality with the experimentally-demonstrated circuit QED system, consisting of two well-separated superconducting charge qubits (SCQs) dispersively coupled to a common one-dimensional transmission line resonator (TLR). Our proposal is based on the joint spectral measurements of the two SCQs, i.e., their quantum states in the computational basis {∣kl>, k,l=0,1}\{|kl>,\,k,l=0,1\}{∣kl>,k,l=0,1} can be measured by detecting the transmission spectra of the driven TLR: each peak marks one of the computational basis and its relative height corresponds to the probability superposed. With these joint spectral measurements, the generated Bell states of the two SCQs can be robustly confirmed without the standard tomographic technique. Furthermore, the statistical nonlocal-correlations between these two distant qubits can be directly read out by the joint spectral measurements, and consequently the Bell's inequality can be tested by sequentially measuring the relevant correlations related to the suitably-selected sets of the classical local variables {θj,θj′,j=1,2}\{θ_j,θ_j', j=1,2\}{θj​,θj′​,j=1,2}. The experimental challenges of our proposal are also analyzed.
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.