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arXiv:1312.1102 · Scientific Reports

Experimental linear-optics simulation of multipartite non-locality in the ground state of a quantum Ising ring

Adeline Orieux, Joelle Boutari, Marco Barbieri, Mauro Paternostro, Paolo Mataloni

Published Nov 24, 2014• 10 citations
arXivHTMLPDF

Abstract

Critical phenomena involve structural changes in the correlations of its constituents. Such changes can be reproduced and characterized in quantum simulators able to tackle medium-to-large-size systems. We demonstrate these concepts by engineering the ground state of a three-spin Ising ring by using a pair of entangled photons. The effect of a simulated magnetic field, leading to a critical modification of the correlations within the ring, is analysed by studying two- and three-spin entanglement. In particular, we connect the violation of a multipartite Bell inequality with the amount of tripartite entanglement in our ring.

DOI
10.1038/srep07184

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Critical phenomena involve structural changes in the correlations of its constituents. Such changes can be reproduced and characterized in quantum simulators able to tackle medium-to-large-size systems. We demonstrate these concepts by engineering the ground state of a three-spin Ising ring by using a pair of entangled photons. The effect of a simulated magnetic field, leading to a critical modification of the correlations within the ring, is analysed by studying two- and three-spin entanglement. In particular, we connect the violation of a multipartite Bell inequality with the amount of tripartite entanglement in our ring.
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We find non-localities, violation of local realism, in the many-body ground states of spin-1 XXZ chain with on-site anisotropy. In order to identify the non-localities in higher spin systems, we exploit the generalized version of multipartite Bell-type inequalities which characterize symmetric entangled states under the most general settings via combination of high-order correlations. For a given set of unbiased measurements, we obtain a sharp violation of the multipartite Bell-type inequality at the vicinity of the quantum criticality, a type of the first-order, in the regime of large exchanges and strong on-site anisotropies. It signifies that impossibility of local realistic picture is manifested when a system is subjected to quantum phase transition between weekly entangled states via GHZ-like state. Our results provide the first extendible picture on the relationship between the impossibility of local realistic model and many-body quantum phases in higher-spin system as the observable identifies measurable quantities to detect the non-locality on a particular many-body quantum state.
Quantum phase transitions occur when the ground state of a Hamiltonian undergoes qualitative changes with a control parameter changing. In this paper we consider a particular system--an Isng-type spin ring with competing many-body interactions. Depending on the relative strength interactions, the ground state of the system is either a product state or entangled state. We implement the system in a cavity-assisted neutral atomic simulator and study the non-locality and entanglement of the simulated ground state of an Ising-type three-spin ring with the control parameter changing. The simplicity of the setup and its robustness to noise give it a great practicality within the framework of current experimental technology.
We investigate the entanglement properties of finite spin rings, with noncollinear Ising interaction between nearest neighbors. The orientations of the Ising axes are determined either by the spin position within the ring (model AAA) or by the direction of the bond (model BBB). In both cases, the considered spin Hamiltonians have a point-group symmetry instead of the translation invariance that characterizes spin rings with collinear Ising interaction. The ground state of these models exhibit remarkable entanglement properties, resembling Greenberger-Horne-Zeilinger (GHZ)-like states in the absence of an applied magnetic field (model BBB). Besides, the application of a homogeneous magnetic field allows to modify qualitatively the character of the ground-state entanglement, switching from multipartite to pairwise quantum correlations (both models AAA and BBB).
Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems. The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain. In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations. Chapter 4 contains a digital…