Relevant bibliographies by topics / Geometric Measure of Entanglement

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Geometric Measure of Entanglement'

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Published: 1 February 2025

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Journal articles on the topic "Geometric Measure of Entanglement"

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Cao, Ya, and An Min Wang. "Revised geometric measure of entanglement." Journal of Physics A: Mathematical and Theoretical 40, no. 13 (March 14, 2007): 3507–37. http://dx.doi.org/10.1088/1751-8113/40/13/014.

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Wei, T. C., M. Ericsson, P. M. Goldbart, and W. J. Munro. "Connections between relative entropy of entanglement and geometric measure of entanglement." Quantum Information and Computation 4, no. 4 (July 2004): 252–72. http://dx.doi.org/10.26421/qic4.4-2.

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As two of the most important entanglement measures---the entanglement of formation and the entanglement of distillation---have so far been limited to bipartite settings, the study of other entanglement measures for multipartite systems appears necessary. Here, connections between two other entanglement measures---the relative entropy of entanglement and the geometric measure of entanglement---are investigated. It is found that for arbitrary pure states the latter gives rise to a lower bound on the former. For certain pure states, some bipartite and some multipartite, this lower bound is saturated, and thus their relative entropy of entanglement can be found analytically in terms of their known geometric measure of entanglement. For certain mixed states, upper bounds on the relative entropy of entanglement are also established. Numerical evidence strongly suggests that these upper bounds are tight, i.e., they are actually the relative entropy of entanglement.
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Guo, Yu, Yanping Jia, Xinping Li, and Lizhong Huang. "Genuine multipartite entanglement measure." Journal of Physics A: Mathematical and Theoretical 55, no. 14 (March 9, 2022): 145303. http://dx.doi.org/10.1088/1751-8121/ac5649.

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Abstract Quantifying genuine entanglement is a crucial task in quantum information theory. In this work, we give an approach of constituting genuine m-partite entanglement measures from any bipartite entanglement and any k-partite entanglement measure, 3 ⩽ k < m. In addition, as a complement to the three-qubit concurrence triangle proposed in (Phys. Rev. Lett. 127 040403), we show that the triangle relation is also valid for any continuous entanglement measure and system with any dimension. We also discuss the tetrahedron structure for the four-partite system via the triangle relation associated with tripartite and bipartite entanglement respectively. For multipartite system that contains more than four parties, there is no symmetric geometric structure as that of tri- and four-partite cases.
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Shi, Xian, Lin Chen, and Yixuan Liang. "Quantifying the entanglement of quantum states under the geometric method." Physica Scripta 98, no. 1 (December 7, 2022): 015103. http://dx.doi.org/10.1088/1402-4896/aca56e.

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Abstract Quantifying entanglement is an important issue in quantum information theory. Here we consider the entanglement measures through the trace norm in terms of two methods, the modified measure and the extended measure for bipartite states. We present the analytical formula for the pure states in terms of the modified measure and the mixed states of two-qubit systems for the extended measure. We also generalize the modified measure from bipartite states to tripartite states.
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Chang, Haixia, Vehbi E. Paksoy, and Fuzhen Zhang. "Interpretation of generalized matrix functions via geometric measure of quantum entanglement." International Journal of Quantum Information 13, no. 07 (October 2015): 1550049. http://dx.doi.org/10.1142/s0219749915500495.

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By using representation theory and irreducible characters of the symmetric group, we introduce character dependent states and study their entanglement via geometric measure. We also present a geometric interpretation of generalized matrix functions via this entanglement analysis.
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Buchholz, Lars Erik, Tobias Moroder, and Otfried Gühne. "Evaluating the geometric measure of multiparticle entanglement." Annalen der Physik 528, no. 3-4 (December 9, 2015): 278–87. http://dx.doi.org/10.1002/andp.201500293.

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Zhang, Meiming, and Naihuan Jing. "Tighter monogamy relations of entanglement measures based on fidelity." Laser Physics Letters 19, no. 8 (July 11, 2022): 085205. http://dx.doi.org/10.1088/1612-202x/ac772e.

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Abstract We study the Bures measure of entanglement and the geometric measure of entanglement as special cases of entanglement measures based on fidelity, and find their tighter monogamy inequalities over tri-qubit systems as well as multi-qubit systems. Furthermore, we derive the monogamy inequality of concurrence for qudit quantum systems by projecting higher-dimensional states to qubit substates.
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Paz-Silva, Gerardo A., and John H. Reina. "Geometric multipartite entanglement measures." Physics Letters A 365, no. 1-2 (May 2007): 64–69. http://dx.doi.org/10.1016/j.physleta.2006.12.065.

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Jang, Kap Soo, MuSeong Kim, and DaeKil Park. "Phase-factor Dependence of the Geometric Entanglement Measure." Journal of the Korean Physical Society 58, no. 5 (May 13, 2011): 1058–75. http://dx.doi.org/10.3938/jkps.58.1058.

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KAZAKOV, A. YA. "THE GEOMETRIC MEASURE OF ENTANGLEMENT OF THREE-PARTITE PURE STATES." International Journal of Quantum Information 04, no. 06 (December 2006): 907–15. http://dx.doi.org/10.1142/s0219749906002286.

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As a measure of entanglement of three-partite pure state, the distance between this state and a set of fully disentangled states is considered. This distance can be calculated for W-class three-qubit pure states and generalized GHZ-states in explicit analytical form. For general multipartite pure states, the distance up to the set of 1-disentangled states is derived. This value can be considered as a low bound for the entanglement of multipartite pure state.
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Dissertations / Theses on the topic "Geometric Measure of Entanglement"

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Amouzou, Grâce Dorcas Akpéné. "Etude de l’intrication par les polynômes de Mermin : application aux algorithmes quantiques." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2024. http://www.theses.fr/2024UBFCK063.

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Cette thèse explore la mesure de l'intrication dans certains états hypergraphiques, dans certains algorithmes quantiques tels que les algorithmes quantiques d'estimation de phase et de comptage, ainsi que dans les circuits d'agents réactifs, à l'aide de la mesure géométrique de l'intrication, d'outils issus des polynômes de Mermin et des matrices de coefficients. L'intrication est un concept présent en physique quantique qui n'a pas d'équivalent connu à ce jour en physique classique.Le coeur de notre recherche repose sur la mise en place de dispositifs de détection et de mesure de l'intrication afin d'étudier des états quantiques du point de vue de l'intrication.Dans cette optique, des calculs sont d'abord effectués numériquement puis sur simulateur et ordinateur quantiques. Effectivement, trois des outils exploités sont implémentables sur machine quantique, ce qui permet de comparer les résultats théoriques et "réels"
This thesis explores the measurement of entanglement in certain hypergraph states, in certain quantum algorithms like the Quantum Phase estimation and Counting algorithms as well as in reactive agent circuits, using the geometric measurement of entanglement, tools from Mermin polynomials and coefficient matrices. Entanglement is a concept present in quantum physics that has no known equivalent to date in classical physics.The core of our research is based on the implementation of entanglement detection and measurement devices in order to study quantum states from the point of view of entanglement.With this in mind, calculations are first carried out numerically and then on a quantum simulator and computer. Indeed, three of the tools used can be implemented on a quantum machine, which allows us to compare theoretical and "real" results
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Teng, Peiyuan. "Tensor network and neural network methods in physical systems." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524836522115804.

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Fuentes, Guridi Ivette. "Entanglement and geometric phases in light-matter interactions." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.400562.

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Gunhan, Ali Can. "Environmental Effects On Quantum Geometric Phase And Quantum Entanglement." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12609450/index.pdf.

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We investigate the geometric phase (GP) acquired by the states of a spin-1/2 nucleus which is subject to a static magnetic field. This nucleus as the carrier system of GP, is taken as coupled to a dissipative environment, so that it evolves non-unitarily. We study the effects of different characteristics of different environments on GP as nucleus evolves in time. We showed that magnetic field strength is the primary physical parameter that determines the stability of GP
its stability decreases as the magnetic field strength increases. (By decrease in stability what we mean is the increase in the time rate of change of GP.) We showed that this decrease can be very rapid, and so it could be impossible to make use of it as a quantum logic gate in quantum information theory (QIT). To see if these behaviors differ in different environments, we analyze the same system for a fixed temperature environment which is under the influence of an electromagnetic field in a squeezed state. We find that the general dependence of GP on magnetic field does not change, but this time the effects are smoother. Namely, increase in magnetic field decreases the stability of GP also for in this environment
but this decrease is slower in comparison with the former case, and furthermore it occurs gradually. As a second problem we examine the entanglement of two atoms, which can be used as a two-qubit system in QIT. The entanglement is induced by an external quantum system. Both two-level atoms are coupled to a third two-level system by dipole-dipole interaction. The two atoms are assumed to be in ordinary vacuum and the third system is taken as influenced by a certain environment. We examined different types of environments. We show that the steady-state bipartite entanglement can be achieved in case the environment is a strongly fluctuating, that is a squeezed-vacuum, while it is not possible for a thermalized environment.
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Hartley, Julian. "Aspects of entanglement and geometric phase in quantum information." Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.420622.

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Johansson, Markus. "Entanglement and Quantum Computation from a Geometric and Topological Perspective." Doctoral thesis, Uppsala universitet, Teoretisk kemi, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-173120.

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In this thesis we investigate geometric and topological structures in the context of entanglement and quantum computation. A parallel transport condition is introduced in the context of Franson interferometry based on the maximization of two-particle coincidence intensity. The dependence on correlations is investigated and it is found that the holonomy group is in general non-Abelian, but Abelian for uncorrelated systems. It is found that this framework contains a parallel transport condition developed by Levay in the case of two-qubit systems undergoing local SU(2) evolutions. Global phase factors of topological origin, resulting from cyclic local SU(2) evolution, called topological phases, are investigated in the context of multi-qubit systems. These phases originate from the topological structure of the local SU(2)-orbits and are an attribute of most entangled multi-qubit systems. The relation between topological phases and SLOCC-invariant polynomials is discussed. A general method to find the values of the topological phases in an n-qubit system is described. A non-adiabatic generalization of holonomic quantum computation is developed in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. It is shown how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing transitions in a generic three-level Λ configuration. The robustness of the proposed scheme to different sources of error is investigated through numerical simulation. It is found that the gates can be made robust to a variety of errors if the operation time of the gate can be made sufficiently short. This scheme opens up for universal holonomic quantum computation on qubits characterized by short coherence times.
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Villa, E. "Methods of geometric measure theory in stochastic geometry." Doctoral thesis, Università degli Studi di Milano, 2007. http://hdl.handle.net/2434/28369.

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All the results of the present thesis have been obtained facing problems related to the study of the so called birth-and-growth stochastic processes, relevant in several real applications, like crystallization processes, tumour growth, angiogenesis, etc. We have introduced a Delta formalism, à la Dirac-Schwartz, for the description of random measures associated with random closed sets in R^d of lower dimensions, such that the usual Dirac delta at a point follows as particular case, in order to provide a natural framework for deriving evolution equations for mean densities at integer Hausdorff dimensions in terms of the relevant kinetic parameters associated to a given birth-and-growth process. In this context connections with the concepts of hazard functions and spherical contact distribution functions, together with local Steiner formulas at first order have been studied and, under suitable general conditions on the resulting random growing set, we may write evolution equations of the mean volume density in terms of the growing rate and of the mean surface density. To this end we have introduced definitions of discrete, continuous and absolutely continuous random closed set, which extend the standard well known definitions for random variables. Further, since in many real applications such as fibre processes, n-facets of random tessellations several problems are related to the estimation of such mean densities, in order to face such problems in the general setting of spatially inhomogeneous processes, we have analyzed an approximation of mean densities for sufficiently regular random closed sets, such that some known results in literature follow as particular cases.
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Hudgell, Sarahann. "Produce software to measure the geometric properties of airways /." Leeds : University of Leeds, School of Computer Studies, 2008. http://www.comp.leeds.ac.uk/fyproj/reports/0708/Hudgell.pdf.

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Vedovato, Mattia. "Some variational and geometric problems on metric measure spaces." Doctoral thesis, Università degli studi di Trento, 2022. https://hdl.handle.net/11572/337379.

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In this Thesis, we analyze three variational and geometric problems, that extend classical Euclidean issues of the calculus of variations to more general classes of spaces. The results we outline are based on the articles [Ved21; MV21] and on a forthcoming joint work with Nicolussi Golo and Serra Cassano. In the first place, in Chapter 1 we provide a general introduction to metric measure spaces and some of their properties. In Chapter 2 we extend the classical Talenti’s comparison theorem for elliptic equations to the setting of RCD(K,N) spaces: in addition the the generalization of Talenti’s inequality, we will prove that the result is rigid, in the sense that equality forces the space to have a symmetric structure, and stable. Chapter 3 is devoted to the study of the Bernstein problem for intrinsic graphs in the first Heisenberg group H^1: we will show that under mild assumptions on the regularity any stationary and stable solution to the minimal surface equation needs to be intrinsically affine. Finally, in Chapter 4 we study the dimension and structure of the singular set for p-harmonic maps taking values in a Riemannian manifold.
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CASTELPIETRA, MARCO. "Metric, geometric and measure theoretic properties of nonsmooth value functions." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2007. http://hdl.handle.net/2108/202601.

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La funzione valore è un nodo centrale del controllo ottimo. `E noto che la funzione valore può essere irregolare anche per sistemi molto regolari. Pertanto l’analisi non liscia diviene un importante strumento per studiarne le proprietà, anche grazie alle numerose connessioni con la semiconcavità. Sotto opportune ipotesi, la funzione valore è localmente semiconcava. Questa proprietà è connessa anche con la proprietà di sfera interna dei suoi insiemi di livello e dei loro perimetri. In questa tesi introduciamo l’analisi non-liscia e le sue connessioni con funzioni semiconcave ed insiemi di perimetro finito. Descriviamo i sistemi di controllo ed introduciamo le proprietà basilari della funzione tempo minimo T(x) e della funzione valore V (x). Usando il principio del massimo, estendiamo alcuni risultati noti di sfera interna per gli insiemi raggiungibili A(T), al caso non-autonomo ed ai sistemi con costo corrente non costante. Questa proprietà ci permette di ottenere delle stime sui perimetri per alcuni sistemi di controllo. Infine queste proprietà degli insiemi raggiungibili possono essere estese agli insiemi di livello della funzione valore, e, sotto alcune ipotesi di controllabilità otteniamo anche semiconcavità locale per V (x). Inoltre studiamo anche sistemi di controllo vincolati. Nei sistemi vincolati la funzione valore perde regolarità. Infatti, quando una traiettoria tocca il bordo del vincolo Ω, si presentano delle singolarità. Questi effetti sono evidenziati anche dal principio del massimo, che produce un termine aggiuntivo di misura(eventualmente discontinuo), quando una traiettoria tocca il bordo ∂Ω. E la funzione valore perde la semiconcavità, anche per sistemi particolarmente semplici. Ma siamo in grado di recuperare lipschitzianità per il tempo minimo, ed enunciare il principio del massimo esplicitando il termine di bordo. In questo modo otteniamo delle particolari proprietà di sfera interna, e quindi anche stime sui perimetri, per gli insiemi raggiungibili.
The value function is a focal point in optimal control theory. It is a known fact that the value function can be nonsmooth even with very smooth data. So, nonsmooth analysis is a useful tool to study its regularity. Semiconcavity is a regularity property, with some fine connection with nonsmooth analysis. Under appropriate assumptions, the value function is locally semiconcave. This property is connected with the interior sphere property of its level sets and their perimeters. In this thesis we introduce basic concepts of nonsmooth analysis and their connections with semiconcave functions, and sets of finite perimeter. We describe control systems, and we introduce the basic properties of the minimum time function T(x) and of the value function V (x). Then, using maximum principle, we extend some known results of interior sphere property for the attainable setsA(t), to the nonautonomous case and to systems with nonconstant running cost L. This property allow us to obtain some fine perimeter estimates for some class of control systems. Finally these regularity properties of the attainable sets can be extended to the level sets of the value function, and, with some controllability assumption, we also obtain a local semiconcavity for V (x). Moreoverwestudycontrolsystemswithstateconstraints. Inconstrained systems we loose many of regularity properties related to the value function. In fact, when a trajectory of control system touches the boundary of the constraint set Ω, some singularity effect occurs. This effect is clear even in the statement of the maximum principle. Indeed, due to the times in which a trajectory stays on ∂Ω, a measure boundary term (possibly, discontinuous) appears. So, we have no more semiconcavity for the value function, even for very simple control systems. But we recover Lipschitz continuity for the minimum time and we rewrite the constrained maximum principle with an explicit boundary term. We also obtain a kind of interior sphere property, and perimeter estimates for the attainable sets for some class of control systems.
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Books on the topic "Geometric Measure of Entanglement"

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Federer, Herbert. Geometric Measure Theory. Edited by B. Eckmann and B. L. van der Waerden. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2.

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Federer, Herbert. Geometric measure theory. Berlin: Springer, 1996.

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Ambrosio, Luigi, ed. Geometric Measure Theory and Real Analysis. Pisa: Scuola Normale Superiore, 2014. http://dx.doi.org/10.1007/978-88-7642-523-3.

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Bombieri, E., ed. Geometric Measure Theory and Minimal Surfaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-10970-6.

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service), SpringerLink (Online, ed. Geometric Measure Theory and Minimal Surfaces. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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Morgan, Frank. Geometric measure theory: A beginner's guide. Boston: Academic Press, 1988.

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De Philippis, Guido, Xavier Ros-Oton, and Georg S. Weiss. Geometric Measure Theory and Free Boundary Problems. Edited by Matteo Focardi and Emanuele Spadaro. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65799-4.

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Figalli, Alessio, Ireneo Peral, and Enrico Valdinoci. Partial Differential Equations and Geometric Measure Theory. Edited by Alberto Farina and Enrico Valdinoci. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74042-3.

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1949-, Parks Harold R., ed. Geometric integration theory. Boston, Mass: Birkhäuser, 2008.

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Allard, William, and Frederick Almgren, eds. Geometric Measure Theory and the Calculus of Variations. Providence, Rhode Island: American Mathematical Society, 1986. http://dx.doi.org/10.1090/pspum/044.

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Book chapters on the topic "Geometric Measure of Entanglement"

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Marín, Juan, José Martell, Dorina Mitrea, Irina Mitrea, and Marius Mitrea. "Geometric Measure Theory." In Progress in Mathematics, 27–161. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-08234-4_2.

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Federer, Herbert. "General measure theory." In Geometric Measure Theory, 50–206. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_3.

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Federer, Herbert. "Introduction." In Geometric Measure Theory, 1–7. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_1.

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Federer, Herbert. "Grassmann algebra." In Geometric Measure Theory, 8–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_2.

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Federer, Herbert. "Rectifiability." In Geometric Measure Theory, 207–340. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_4.

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Federer, Herbert. "Homological integration theory." In Geometric Measure Theory, 341–512. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_5.

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Federer, Herbert. "Applications to the calculus of variations." In Geometric Measure Theory, 513–654. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62010-2_6.

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Bertlmann, Reinhold A., and Nicolai Friis. "Quantification and Conversion of Entanglement." In Modern Quantum Theory, 485–541. Oxford University PressOxford, 2023. http://dx.doi.org/10.1093/oso/9780199683338.003.0016.

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Abstract In this chapter the quantification of entanglement is discussed. Beginning with the pure-state entanglement measure called the entropy of entanglement, we discuss the paradigm of local operations and classical communication (LOCC) and its relation to majorization via Nielsen’s majorization theorem. We then turn to the asymptotic setting and discuss the formation and distillation of entanglement and the related entanglement measures: entanglement cost and distillable entanglement, and we examine the notions of distillability and bound entanglement. This brings us to a more general discussion of entanglement measures and monotones, and their desired properties, during which we present the entanglement of formation and concurrence, squashed entanglement, as well as the tangle and its relation to monogamy of entanglement, but also quantities like the relative entropy of entanglement, the Hilbert-Schmidt measure, and the (logarithmic) negativity. Finally we turn to the construction of entanglement witnesses and their geometric interpretation via the Bertlmann-Narnhofer-Thirring theorem
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Baggott, Jim. "Complementarity and entanglement." In Beyond measure, 181–204. Oxford University PressOxford, 2003. http://dx.doi.org/10.1093/oso/9780198529279.003.0010.

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Abstract The results of the experiments described in the last chapter all point fairly unambiguously to a reality that is decidedly non-local in nature, at least in the quantum domain. Of course, these are results that come as no surprise to those willing to accept one of the most fundamental principles of the Copenhagen interpretation — that quantum phenomena are describable only in terms of the dual classical physical concepts of waves and particles. The wave properties of quantum entities lend them inherently non-local characteristics, and it is only when we forcibly ‘collapse’ the wave function by making a measurement that we are taken aback by what appears to be contradictory or counter-intuitive behaviour.
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Jozsa, Richard. "Entanglement and Quantum Computation." In The Geometric Universe, 369–79. Oxford University PressOxford, 1998. http://dx.doi.org/10.1093/oso/9780198500599.003.0027.

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Abstract The phenomenon of quantum entanglement is perhaps the most enigmatic feature of the formalism of quantum theory. It underlies many of the most curious and controversial aspects of the quantum mechanical description of the world. Penrose (1994) gives a delightful and accessible account of entanglement illustrated by some of its extraordinary manifestations. Many of the best known features depend on issues of non-locality. These include the seminal work of Einstein, Podolsky and Rosen (1935), Bell’s work (1964) on the EPR singlet state, properties of the GHZ state (Greenberger et al. 1989; Mermin 1990) and Penrose’s dodecahedra (Penrose 1994). In this paper we describe a new feature of entanglement which is entirely independent of the auxiliary notion of non-locality.
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Conference papers on the topic "Geometric Measure of Entanglement"

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Huertas, Samuel, Daniel Peláez, Valentina López, Laura Bravo, and Romón Castañeda. "Spatial Entanglement of Geometric States of Ordinary Space in Non-paraxial Inteference." In 2024 XVIII National Meeting on Optics and the IX Andean and Caribbean Conference on Optics and its Applications (ENO-CANCOA), 1–4. IEEE, 2024. http://dx.doi.org/10.1109/eno-cancoa61307.2024.10751559.

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Seshadri, Suparna, Karthik V. Myilswamy, Zhao-Hui Ma, Yu-Ping Huang, and Andrew M. Weiner. "Measuring frequency-bin entanglement from a quasi-phase-matched lithium niobate microring." In CLEO: Fundamental Science, FTu4F.3. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_fs.2024.ftu4f.3.

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We employ phase modulation to measure the phase coherence between 31.75 GHz-spaced frequency bins in a biphoton frequency comb generated from an integrated quasi-phase-matched thin-film lithium niobate microresonator.
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Klaver, Yvan, Randy te Morsche, Batoul Hashemi, Bruno L. Segat Frare, Pooya Torab Ahmadi, Niloofar Majidian Taleghani, Evan Jonker, et al. "Enhanced stimulated Brillouin scattering in tellurite covered silicon nitride waveguides via geometric and cladding engineering." In CLEO: Science and Innovations, STh4C.1. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_si.2024.sth4c.1.

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We measure Brillouin-scattering in geometrically and cladding engineered tellurite covered silicon nitride waveguide in which we report gain values of 80.9 m–1W–1 and 76.3 m–1W–1, a 150 times improvement over previous silicon nitride based waveguides.
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Życzkowski, Karol. "Geometry of Quantum Entanglement." In Workshop on Entanglement and Quantum Decoherence. Washington, D.C.: Optica Publishing Group, 2008. http://dx.doi.org/10.1364/weqd.2008.embs3.

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Abstract:
A geometric approach to investigation of quantum entanglement is advocated. Analyzing the space of pure states of a bipartite system we show how an entanglement measure of a gives state can be related to its distance to the closest separable state. We study geometry of the (N2 - 1)-dimensional convex body of mixed quantum states acting on an N-dimensional Hilbert space and demonstrate that it belongs to the class of sets of a constant height. The same property characterizes the set of all separable states of a two-qubit system. These results contribute to our understanding of quantum entanglement and its dynamics.
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5

Susulovska, N. A., and Kh P. Gnatenko. "Quantifying Geometric Measure of Entanglement of Multi-qubit Graph States on the IBM’s Quantum Computer." In 2021 IEEE International Conference on Quantum Computing and Engineering (QCE). IEEE, 2021. http://dx.doi.org/10.1109/qce52317.2021.00080.

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6

Beigi, Salman. "Maximal entanglement — A new measure of entanglement." In 2014 Iran Workshop on Communication and Information Theory (IWCIT). IEEE, 2014. http://dx.doi.org/10.1109/iwcit.2014.6842486.

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7

Xie, Songbo, and Joseph H. Eberly. "Multi-Photonic Entanglement, A Geometric Approach." In Frontiers in Optics. Washington, D.C.: OSA, 2021. http://dx.doi.org/10.1364/fio.2021.fth6d.6.

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8

Jha, Anand K., Mehul Malik, and Robert W. Boyd. "Exploring Energy-Time Entanglement Using Geometric Phase." In International Quantum Electronics Conference. Washington, D.C.: OSA, 2009. http://dx.doi.org/10.1364/iqec.2009.iwf7.

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9

Toro, Tatiana. "Potential Analysis Meets Geometric Measure Theory." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0107.

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10

Jack, B., J. Leach, J. Romero, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett. "Spatial Light Modulators to Measure Entanglement Between Spatial States." In Frontiers in Optics. Washington, D.C.: OSA, 2009. http://dx.doi.org/10.1364/fio.2009.jtub4.

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