Relevant bibliographies by topics / Quantum operator algebras

Contents

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

Academic literature on the topic 'Quantum operator algebras'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Quantum operator algebras"

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Zhan, Qiuyan. "Some Operators on Quantum B-Algebras." Symmetry 13, no. 8 (2021): 1381. http://dx.doi.org/10.3390/sym13081381.

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The aim of this paper is to investigate several operators on quantum B-algebras. At first, we introduce closure and interior operators on quantum B-algebras and consider their relations on bounded quantum B-algebras. Furthermore, we discuss very true operators on quantum B-algebras by three cases via the unit element, and present some similar conclusions and different results. Finally, by constructing a very true operator on a quotient very true perfect quantum B-algebra, we establish a homomorphism theorem on very true perfect quantum B-algebras.
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Bock, Wolfgang, Janeth Canama, and Gaudencio Petalcorin. "On Solvable Lie Algebras of White Noise Operators." Symmetry 14, no. 11 (2022): 2301. http://dx.doi.org/10.3390/sym14112301.

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We characterize the dimension of Lie algebras of white noise operators containing the quantum white noise derivatives of the conservation operator. We establish isomorphisms to filiform Lie algebras, Engel-type algebras, and solvable Lie algebras with Heisenberg nilradical and Abelian nilradical. A new class of solvable Lie algebras is proposed, those having an Engel-type algebra as nilradical. This arises in white noise analysis as a 2n+3-dimensional Lie algebra containing the identity operator, annihilation operators, creation operators (Heisenberg algebra), number operator, and Gross Laplac
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Pavlakos, Panaiotis K. "Integral representation theorems in partially ordered vector spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 51, no. 2 (1991): 187–215. http://dx.doi.org/10.1017/s1446788700034194.

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AbstractDefining a Radon-type integration process we extend the Alexandroff, Fichtengolts-KantorovichHildebrandt and Riesz integral representation theorems in partially ordered vector spaces.We also identify some classes of operators with other classes of operator-valued set functions, the correspondence between operator and operator-valued set function being given by integration.All these established results can be immediately applied in C* -algebras (especially in W* -algebras and AW* -algebras of type I), in Jordan algebras, in partially ordered involutory (O*-)algebras, in semifields, in q
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ISAEV, A. P., and O. OGIEVETSKY. "BRST OPERATOR FOR QUANTUM LIE ALGEBRAS: EXPLICIT FORMULA." International Journal of Modern Physics A 19, supp02 (2004): 240–47. http://dx.doi.org/10.1142/s0217751x04020440.

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We continue our study of quantum Lie algebras, an important class of quadratic algebras arising in the Woronowicz calculus on a quantum group. Quantum Lie algebras are generalizations of Lie (super)algebras. Many notions from the theory of Lie (super)algebras admit "quantum" analogues. In particular, there is a BRST operator Q(Q2=0) which generates the differential in the Woronowicz theory and gives information about (co)homologies of quantum Lie algebras. In our previous papers a recurrence relation for the operator Q for quantum Lie algebras was given. Here we solve this recurrence relation
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CASTRO, OSVALDO OSUNA, та ELMAR WAGNER. "AN OPERATOR-THEORETIC APPROACH TO INVARIANT INTEGRALS ON QUANTUM HOMOGENEOUS SLn+1(ℝ)-SPACES". International Journal of Geometric Methods in Modern Physics 09, № 01 (2012): 1250012. http://dx.doi.org/10.1142/s0219887812500120.

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We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kürsten and the second author. The quantum spaces are chosen such that their coordinate algebras do not admit bounded Hilbert space representations and their self-adjoint generators have continuous spectrum. Operator algebras of trace class operators are associated to the coordinate algebras which allow interpretations as rapidly decreasing functions and as finite functions. The invariant integral is defined as a trace functional which generalizes the well-kn
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Lian, Bong H., and Gregg J. Zuckerman. "Commutative quantum operator algebras." Journal of Pure and Applied Algebra 100, no. 1-3 (1995): 117–39. http://dx.doi.org/10.1016/0022-4049(95)00053-y.

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Kribs, David W., Jeremy Livick, Mike I. Nelson, Rajesh Perira, and Mizanur Rahaman. "Quantum complementarity and operator structures." Quantum Information and Computation 19, no. 1&2 (2019): 67–83. http://dx.doi.org/10.26421/qic19.1-2-5.

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We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private operator algebras, and operator spaces such as multiplicative domains and nullspaces of quantum channels and their complementary maps. For the case of privatizing to quantum states, we also derive dimension inequalities on the associated operator algebras that further quantify the trade-off between correction and privacy.
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Frønsdal, C., and A. Galindo. "8-Vertex Correlation Functions and Twist Covariance of q-KZ Equation." Reviews in Mathematical Physics 10, no. 08 (1998): 1027–59. http://dx.doi.org/10.1142/s0129055x98000331.

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We study the vertex operators Φ(z) associated with standard quantum groups. The element Z=RR t is a "Casimir operator" for quantized Kac–Moody algebras and the quantum Knizhnik–Zamolodchikov (q-KZ) equation is interpreted as the statement :ZΦ(z):=Φ(z). We study the covariance of the q-KZ equation under twisting, first within the category of Hopf algebras, and then in the wider context of quasi Hopf algebras. We obtain the intertwining operators associated with the elliptic R-matrix and calculate the two-point correlation function for the eight-vertex model.
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LI, HAISHENG. "CONSTRUCTING QUANTUM VERTEX ALGEBRAS." International Journal of Mathematics 17, no. 04 (2006): 441–76. http://dx.doi.org/10.1142/s0129167x06003588.

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This is a sequel to [23]. In this paper, we focus on the construction of quantum vertex algebras over ℂ, whose notion was formulated in [23] with Etingof and Kazhdan's notion of quantum vertex operator algebra (over ℂ[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely, noncommutative) vertex algebra over ℂ, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known ver
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MELJANAC, STJEPAN, MARKO STOJIĆ, and MARIJAN MILEKOVIĆ. "ON PARASTATISTICS DEFINED AS TRIPLE OPERATOR ALGEBRAS." Modern Physics Letters A 13, no. 13 (1998): 995–1005. http://dx.doi.org/10.1142/s0217732398001078.

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Parastatistics, defined as triple operator algebras represented on Fock space, are unified in a simple way using the transition number operators. They are expressed as a normal ordered expansion of creation and annihilation operators. We discuss several examples of parastatistics, particularly Okubo's and Palev's parastatistics connected to many-body Wigner quantum systems and relate them to the notion of extended Haldane statistics.
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Dissertations / Theses on the topic "Quantum operator algebras"

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Oerder, Kyle. "Operator algebras and quantum information." Diss., University of Pretoria, 2020. http://hdl.handle.net/2263/75515.

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The C*-algebra representation of a physical system provides an ideal backdrop for the study of bipartite entanglement, as a natural definition of separability emerges as a direct consequence of the non-abelian nature of quantum systems under this formulation. The focus of this dissertation is the quantification of entanglement for infinite dimensional systems. The use of Choquet’s theory of boundary integrals allows for an integral representation of the states on a C*-algebra and subsequent adaptation of the Convex Roof Measures to infinite dimensional systems. Another measure of entanglement,
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Das, Bata Krishna. "Quantum stochastic analysis in Banach space and operator space." Thesis, Lancaster University, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.660115.

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Sotelo-Campos, J. "An application of operator *-algebras to the theory of quantum measurement." Thesis, Open University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379797.

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Melo, Nolmar. "Uma álgebra de Clifford de assinatura (n,3n) e os operadores densidade da teoria da informação quântica." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306804.

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Orientador: Carlile Campos Lavor<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-17T14:47:27Z (GMT). No. of bitstreams: 1 Melo_Nolmar_D.pdf: 2834013 bytes, checksum: 5639deabb953aa019e4e1c9c905e856d (MD5) Previous issue date: 2011<br>Resumo: Este trabalho apresenta uma linguagem algébrica para dois elementos básicos da teoria da informação quântica (os bits quânticos e os operadores densidade), baseada nas propriedades de uma álgebra de Clifford de assinatura (n,3n). Demonstramos que
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Van, De Ven Christiaan Jozef Farielda. "Quantum Systems and their Classical Limit A C*- Algebraic Approach." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/324358.

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In this thesis we develop a mathematically rigorous framework of the so-called ''classical limit'' of quantum systems and their semi-classical properties. Our methods are based on the theory of strict, also called C*- algebraic deformation quantization. Since this C*-algebraic approach encapsulates both quantum as classical theory in one single framework, it provides, in particular, an excellent setting for studying natural emergent phenomena like spontaneous symmetry breaking (SSB) and phase transitions typically showing up in the classical limit of quantum theories. To this end, several tech
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de, Silva Nadish. "Contextuality and noncommutative geometry in quantum mechanics." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:1ca8995d-b562-426a-ab89-afab3a18dda2.

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It is argued that the geometric dual of a noncommutative operator algebra represents a notion of quantum state space which differs from existing notions by representing observables as maps from states to outcomes rather than from states to distributions on outcomes. A program of solving for an explicitly geometric manifestation of quantum state space by adapting the spectral presheaf, a construction meant to analyze contextuality in quantum mechanics, to derive simple reconstructions of noncommutative topological tools from their topological prototypes is presented. We associate to each unital
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Bostelmann, Henning. "Lokale Algebren und Operatorprodukte am Punkt." Doctoral thesis, [S.l.] : [s.n.], 2000. http://deposit.ddb.de/cgi-bin/dokserv?idn=961247584.

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Bardet, Ivan. "Émergence de dynamiques classiques en probabilité quantique." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSE1071/document.

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Cette thèse se consacre à l'étude de certaines passerelles existantes entre les probabilités dîtes classiques et la théorie des systèmes quantiques ouverts. Le but de la première partie de ce manuscrit est d'étudier l'émergence de bruits classiques dans l'équation de Langevin quantique. Cette équation sert à modéliser l'action d'un bain quantique sur un petit système dans l'approximation markovienne. L'analogue en temps discret de cette équation est décrit par le schéma des interactions quantiques répétées étudier par Stéphane Attal et Yan Pautrat. Dans des travaux antérieurs, Attal et ses col
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Lemeux, Francois. "Sur la théorie des représentations et les algèbres d'opérateurs des produits en couronnes libres." Thesis, Besançon, 2014. http://www.theses.fr/2014BESA2008/document.

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Dans cette thèse, on étudie les propriétés combinatoires, algébriques et analytiques de certains groupes quantiques compacts libres. on prouve au chapitre 2 que les duaux des groupes quantiques de réflexions complexes possèdent, dans la plus part des cas, la propriété d'approximation de Haagerup. au chapitre 3, on décrit les règles de fusion du produit en, couronne libre d'un groupe discret par le groupe quantique des permutations. Pour cela on détermine les espaces d'entrelaceurs entre certaines coreprésentation "basiques" de ces produits en couronnes libres en termes de partitions non croisé
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Lechner, Gandalf. "On the construction of quantum field theories with factorizing S-matrices." Doctoral thesis, [S.l.] : [s.n.], 2006. http://webdoc.sub.gwdg.de/diss/2006/lechner.

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Books on the topic "Quantum operator algebras"

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Evans, David E. Quantum symmetries on operator algebras. Clarendon Press, 1998.

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Soltan, Piotr M. Operator algebras and quantum groups. Edited by Conference on Operator Algebras and Quantum Groups (3rd : 2011 : Będlewo, Poland) and Instytut Matematyczny (Polska Akademia Nauk). Polish Academy of Sciences, Institute of Mathematics, 2012.

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Bratteli, Ola, and Derek W. Robinson. Operator Algebras and Quantum Statistical Mechanics. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-03444-6.

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Bratteli, Ola. Operator algebras and quantum statistical mechanics. 2nd ed. Springer-Verlag, 1987.

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W, Robinson Derek, ed. Operator algebras and quantum statistical mechanics. 2nd ed. Springer-Verlag, 1997.

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Takesaki, Masamichi. Theory of Operator Algebras III. Springer Berlin Heidelberg, 2003.

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Bratteli, Ola, and Derek W. Robinson. Operator Algebras and Quantum Statistical Mechanics 1. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-662-02520-8.

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Inoue, Atsushi. Tomita-Takesaki theory in algebras of unbounded operators. Springer, 1998.

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Carroll, Robert Wayne. Quantum theory, deformation, and integrability. Elsevier Science B.V., 2000.

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Bratteli, Ola. Operator algebras and quantum statistical mechanics 2: Equilibrium states. Models in quantum statistical mechanics. 2nd ed. Springer-Verlag, 1997.

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Book chapters on the topic "Quantum operator algebras"

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Hamhalter, Jan. "Operator Algebras." In Quantum Measure Theory. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0119-8_2.

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Naaijkens, Pieter. "Operator Algebras." In Quantum Spin Systems on Infinite Lattices. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51458-1_2.

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Evans, David E. "Twisted K-Theory and Modular Invariants: I Quantum Doubles of Finite Groups." In Operator Algebras. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-34197-0_6.

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Masuda, Tetsuya, Katsuhisa Mimachi, Yoshiomi Nakagami, Masatoshi Noumi, and Kimio Ueno. "Representation of Quantum Groups." In Mappings of Operator Algebras. Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0453-4_4.

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Rédei, Miklós. "Operator Algebras and Quantum Logic." In Alternative Logics. Do Sciences Need Them? Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05679-0_23.

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Sergeev, Armen. "Quantum Differentials and Function Spaces." In Operator Algebras, Toeplitz Operators and Related Topics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44651-2_24.

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Bratteli, Ola, and Derek W. Robinson. "C*-Algebras and von Neumann Algebras." In Operator Algebras and Quantum Statistical Mechanics 1. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-662-02520-8_2.

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Hudson, R. L. "A Stochastic Double Product in Non-Fock Quantum Stochastic Calculus." In Operator Algebras, Operator Theory and Applications. Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-0346-0174-0_8.

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Bebiano, Natália, João da Providência, and J. P. da Providência. "Non-Hermitian Quantum Mechanics of Bosonic Operators." In Operator Theory, Operator Algebras, and Matrix Theory. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72449-2_3.

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Bratteli, Ola, and Derek W. Robinson. "Quantum Spin Systems." In Operator Algebras and Quantum Statistical Mechanics. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-03444-6_6.

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Conference papers on the topic "Quantum operator algebras"

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Reyes-Lega, Andrés F. "SOME ASPECTS OF OPERATOR ALGEBRAS IN QUANTUM PHYSICS." In Villa de Leyva Summer School. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789814730884_0001.

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LECHNER, GANDALF. "DEFORMATIONS OF OPERATOR ALGEBRAS AND THE CONSTRUCTION OF QUANTUM FIELD THEORIES." In XVIth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814304634_0040.

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Smirnov, Yu F. "Projection operators for Lie algebras, duperalgebras, and quantum algebras." In The XXX Latin American school of physics ELAF: Group theory and its applications. AIP, 1996. http://dx.doi.org/10.1063/1.50219.

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Gao, Li, Marius Junge, and Nicholas LaRacuente. "Operator algebra approach to quantum capacities." In 2016 IEEE International Symposium on Information Theory (ISIT). IEEE, 2016. http://dx.doi.org/10.1109/isit.2016.7541588.

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Goldstein, Stanisław, Hans Jarchow, and Louis E. Labuschagne. "Compactness properties for multiplication operators on von Neumann algebras and their preduals." In Quantum Probability. Institute of Mathematics Polish Academy of Sciences, 2006. http://dx.doi.org/10.4064/bc73-0-12.

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Bertozzini, Paolo. "Categorical Operator Algebraic Foundations of Relational Quantum Theory." In Frontiers of Fundamental Physics 14. Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.224.0206.

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Vieira, Gabriel Mauricio Oswald, Rui Aldé Lopes, Nelson Maculan, and Franklin de Lima Marquezino. "An Algebraic Model for Simulation of Percolation Decoherence on Quantum-Walk-Based Search Algorithms." In Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2024. http://dx.doi.org/10.5753/etc.2024.2031.

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In this paper, we propose a linear algebra based model for percolation noise simulation in quantum-walk-based searches to analyze the impact on the success probability of the search. The model was built to allow an open and simultaneous simulation of any type of noise that represents an edge-break, which we show to be a well-behaved family of permutation matrices that maintain a particular set theory relation when acting as some system evolution operators. The simulation evolves using only linear algebra operations, opening avenues for easier analyses of unexpected observed convergence behavio
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Calvo, M. L., and V. Lakshminarayanan. "Toward a quantum representation for the Fresnel regime in a linear optical system." In OSA Annual Meeting. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.thg5.

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The mathematical treatment involving Fresnel diffraction in compound linear optical systems presents difficulties due to the high degree of oscillations of the Fresnel integral kernel. Also, it is necessary to impose small pupil dimensions on the elements forming the compound system. A revised formulation for the general system having an arbitrary number of elements and generalized pupil functions allows one to represent the kernel in terms of convolution operations. This leads to a compact representation using Lie algebra operators.
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Kalay, Berfin, and Metin Demiralp. "An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2015 (ICCMSE 2015). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4938943.

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Baykara, N. A. "Algebraic function operator expectation value based quantum eigenstate determination: A case of twisted or bent Hamiltonian, or, a spatially univariate quantum system on a curved space." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2015 (ICCMSE 2015). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4938948.

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Reports on the topic "Quantum operator algebras"

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Bond, W., Maria Seale, and Jeffrey Hensley. A dynamic hyperbolic surface model for responsive data mining. Engineer Research and Development Center (U.S.), 2022. http://dx.doi.org/10.21079/11681/43886.

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Data management systems impose structure on data via a static representation schema or data structure. Information from the data is extracted by executing queries based on predefined operators. This paradigm restricts the searchability of the data to concepts and relationships that are known or assumed to exist among the objects. While this is an effective and efficient means of retrieving simple information, we propose that such a structure severely limits the ability to derive breakthrough knowledge that exists in data under the guise of “unknown unknowns.” A dynamic system will alleviate th
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