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David W. Lyons

Bio: David W. Lyons is an academic researcher from Lebanon Valley College. The author has contributed to research in topics: Unitary state & Quantum entanglement. The author has an hindex of 10, co-authored 32 publications receiving 272 citations. Previous affiliations of David W. Lyons include University of North Carolina at Chapel Hill.

Papers
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Journal ArticleDOI
TL;DR: In this article, an elementary introduction to the Hopf Fibration is given, with a discussion of Hopf fibration and its application in algebraic geometry. Mathematics Magazine: Vol. 76, No. 2, pp. 87-98.
Abstract: (2003). An Elementary Introduction to the Hopf Fibration. Mathematics Magazine: Vol. 76, No. 2, pp. 87-98.

74 citations

Journal ArticleDOI
TL;DR: This work points out a connection between local unitary stabilizer subgroups and the property of being determined by reduced density matrices of n-1 qubits.
Abstract: The generalized n-qubit Greenberger-Home-Zeilinger (GHZ) states and their local unitary equivalents are the only states of n qubits that are not uniquely determined among pure states by their reduced density matrices of n - 1 qubits. Thus, among pure states, the generalized GHZ states are the only ones containing information at the n-party level. We point out a connection between local unitary stabilizer subgroups and the property of being determined by reduced density matrices.

28 citations

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TL;DR: This work shows how entanglement types can be detected and distinguished by certain configurations in the hypergraphs from which hypergraph states are constructed, including both continuous and discrete families of symmetries.
Abstract: Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation and quantum error correction. The study of hypergraph states, with their richer multipartite entanglement and other nonlocal properties, has a promising outlook for new insight into multipartite entanglement. We present results analyzing local unitary symmetries of hypergraph states, including both continuous and discrete families of symmetries. In particular, we show how entanglement types can be detected and distinguished by certain configurations in the hypergraphs from which hypergraph states are constructed.

19 citations

Journal ArticleDOI
TL;DR: The generalized Greenberger-Horne-Zeilinger (GHZ) states as discussed by the authors are the only pure states of qubits that are not uniquely determined (among arbitrary states, pure or mixed) by their reduced density matrices of $n\ensuremath{-1$ qubits.
Abstract: The generalized $n$-qubit Greenberger-Horne-Zeilinger (GHZ) states and their local unitary equivalents are the only pure states of $n$ qubits that are not uniquely determined (among arbitrary states, pure or mixed) by their reduced density matrices of $n\ensuremath{-}1$ qubits. Thus, the generalized GHZ states are the only ones containing information at the $n$-party level.

14 citations

Journal ArticleDOI
TL;DR: In this paper, the authors classify, up to local unitary equivalence, the set of $n$-qubit states that are stabilized by the diagonal subgroup of the local unitaries group.
Abstract: We classify, up to local unitary equivalence, the set of $n$-qubit states that is stabilized by the diagonal subgroup of the local unitary group. We exhibit a basis for this set, parameterized by diagrams of nonintersecting chords connecting pairs of points on a circle, and give a criterion for when the stabilizer is precisely the diagonal subgroup and not larger. This investigation is part of a larger program to partially classify entanglement type (local unitary equivalence class) via analysis of stabilizer structure.

14 citations


Cited by
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Journal ArticleDOI
18 Feb 2010
TL;DR: In this article, the system-reservoir dynamics of classical and quantum correlations in the decoherence phenomenon within a two-qubit composite system interacting with two independent environments are examined.
Abstract: We examine the system-reservoir dynamics of classical and quantum correlations in the decoherence phenomenon within a two-qubit composite system interacting with two independent environments. The most common noise channels (amplitude damping, phase damping, bit flip, bit-phase flip, and phase flip) are analyzed. By analytical and numerical analyses we find that, contrary to what is usually stated in the literature, decoherence may occur without entanglement between the system and the environment. We also show that, in some cases, the bipartite quantum correlation initially present in the system is completely evaporated and not transferred to the environments.

246 citations

Journal ArticleDOI
TL;DR: In this article, the physics of topological quantum matter with cold atoms is discussed. But the authors focus on the simulation of the topological invariants and the methods to control parameters in the Hamiltonians of neutral atoms.
Abstract: This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems, which produced both fascinating physics findings and exciting opportunities for applications. Among the physical systems that have been considered to realize and probe these intriguing phases, ultracold atoms become promising platforms due to their high flexibility and controllability. Quantum simulation of topological phases with cold atomic gases is a rapidly evolving field, and recent theoretical and experimental developments reveal that some toy models originally proposed in condensed matter physics have been realized with this artificial quantum system. The purpose of this article is to introduce these developments. The article begins with a tutorial review of topological invariants and the methods to control parameters in the Hamiltonians of neutral atom...

195 citations

Journal ArticleDOI
TL;DR: A review of the physics of topological quantum matter with cold atoms can be found in this paper, where several celebrated models, such as the Su-Schrieffer-Heeger model, Hofstadter-Harper model, Haldane model and Kane-Mele model are discussed.
Abstract: This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems, which produced both fascinating physics findings and exciting opportunities for applications. Among the physical systems that have been considered to realize and probe these intriguing phases, ultracold atoms become promising platforms due to their high flexibility and controllability. Quantum simulation of topological phases with cold atomic gases is a rapidly evolving field, and recent theoretical and experimental developments reveal that some toy models originally proposed in condensed matter physics have been realized with this artificial quantum system. The purpose of this article is to introduce these developments. The article begins with a tutorial review of topological invariants and the methods to control parameters in the Hamiltonians of neutral atoms. Next, topological quantum phases in optical lattices are introduced in some detail, especially several celebrated models, such as the Su-Schrieffer-Heeger model, the Hofstadter-Harper model, the Haldane model and the Kane-Mele model. The theoretical proposals and experimental implementations of these models are discussed. Notably, many of these models cannot be directly realized in conventional solid-state experiments. The newly developed methods for probing the intrinsic properties of the topological phases in cold atom systems are also reviewed. Finally, some topological phases with cold atoms in the continuum and in the presence of interactions are discussed, and an outlook on future work is given.

177 citations

Journal ArticleDOI
TL;DR: This paper analyzes the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under {\em restricted local operation and classical communication} and proposes a new scheme for quantum secret sharing (QSS).
Abstract: In this paper, we analyze the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under restricted local operation and classical communication. Based on this local distinguishability analysis, we propose a quantum secret sharing scheme (which we call LOCC-QSS). Our LOCC-QSS scheme is quite general and cost efficient compared to other schemes. In our scheme, no joint quantum operation is needed to reconstruct the secret. We also present an interesting $(2,n)$-threshold LOCC-QSS scheme, where any two cooperating players, one from each of two disjoint groups of players, can always reconstruct the secret. This LOCC-QSS scheme is quite uncommon, as most $(k,n)$-threshold quantum secret sharing schemes have the restriction $k\ensuremath{\ge}\ensuremath{\lceil}\frac{n}{2}\ensuremath{\rceil}$.

118 citations