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Journal articles on the topic 'Quantum operator algebras'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Takook, Mohammad Vahid. "Quantum de Sitter Geometry." Universe 10, no. 2 (2024): 70. http://dx.doi.org/10.3390/universe10020070.

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Quantum de Sitter geometry is discussed using elementary field operator algebras in Krein space quantization from an observer-independent point of view, i.e., ambient space formalism. In quantum geometry, the conformal sector of the metric becomes a dynamical degree of freedom, which can be written in terms of a massless minimally coupled scalar field. The elementary fields necessary for the construction of quantum geometry are introduced and classified. A complete Krein–Fock space structure for elementary fields is presented using field operator algebras. We conclude that since quantum de Sit

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12

TRAPANI, C. "QUASI *-ALGEBRAS OF OPERATORS AND THEIR APPLICATIONS." Reviews in Mathematical Physics 07, no. 08 (1995): 1303–32. http://dx.doi.org/10.1142/s0129055x95000475.

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The main facts of the theory of quasi*-algebras of operators acting in a rigged Hilbert space are reviewed. The particular case where the rigged Hilbert space is generated by a self-adjoint operator in Hilbert space is examined in more details. A series of applications to quantum theories are discussed.

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13

Hodges, Andrew, and C. V. Sukumar. "Bernoulli, Euler, permutations and quantum algebras." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2086 (2007): 2401–14. http://dx.doi.org/10.1098/rspa.2007.0001.

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The combinatorial properties of the Bernoulli and Euler numbers are interpreted using a new classification of permutations. The classification is naturally described by an operator algebra of a type familiar from quantum theory. It has a duality structure described by an operator satisfying anticommutation relations.

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14

Zanardi, Paolo. "Quantum scrambling of observable algebras." Quantum 6 (March 11, 2022): 666. http://dx.doi.org/10.22331/q-2022-03-11-666.

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In this paper we describe an algebraic/geometrical approach to quantum scrambling. Generalized quantum subsystems are described by an hermitian-closed unital subalgebra A of operators evolving through a unitary channel. Qualitatively, quantum scrambling is defined by how the associated physical degrees of freedom get mixed up with others by the dynamics. Quantitatively, this is accomplished by introducing a measure, the geometric algebra anti-correlator (GAAC), of the self-orthogonalization of the commutant of A induced by the dynamics. This approach extends and unifies averaged bipartite OTOC

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15

PINTO, ERIC, MARCO A. S. TRINDADE, and J. D. M. VIANNA. "QUASITRIANGULAR HOPF ALGEBRAS, BRAID GROUPS AND QUANTUM ENTANGLEMENT." International Journal of Quantum Information 11, no. 07 (2013): 1350065. http://dx.doi.org/10.1142/s0219749913500652.

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The aim of the paper is to provide a method to obtain representations of the braid group through a set of quasitriangular Hopf algebras. In particular, these algebras may be derived from group algebras of cyclic groups with additional algebraic structures. In this context, by using the flip operator, it is possible to construct R-matrices that can be regarded as quantum logic gates capable of preserving quantum entanglement.

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16

MAJID, S. "QUANTUM RANDOM WALKS AND TIME REVERSAL." International Journal of Modern Physics A 08, no. 25 (1993): 4521–45. http://dx.doi.org/10.1142/s0217751x93001818.

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Classical random walks and Markov processes are easily described by Hopf algebras. It is also known that groups and Hopf algebras (quantum groups) lead to classical and quantum diffusions. We study here the more primitive notion of a quantum random walk associated with a general Hopf algebra and show that it has a simple physical interpretation in quantum mechanics. This is by means of a representation theorem motivated from the theory of Kac algebras: If H is any Hopf algebra, it may be realized in Lin(H) in such a way that Δh=W(h⊗1)W−1 for an operator W. This W is interpreted as the time evo

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17

Jones, Vaughan F. R. "Book Review: Quantum symmetries on operator algebras." Bulletin of the American Mathematical Society 38, no. 03 (2001): 369–78. http://dx.doi.org/10.1090/s0273-0979-01-00906-5.

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18

Levick, Jeremy, Tomas Jochym-O’Connor, David W. Kribs, Raymond Laflamme, and Rajesh Pereira. "Private quantum subsystems and quasiorthogonal operator algebras." Journal of Physics A: Mathematical and Theoretical 49, no. 12 (2016): 125302. http://dx.doi.org/10.1088/1751-8113/49/12/125302.

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19

Yu, Zurong. "q-Usui operator of some quantum algebras." Physics Letters A 162, no. 1 (1992): 5–6. http://dx.doi.org/10.1016/0375-9601(92)90947-k.

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20

Heunen, Chris, Nicolaas P. Landsman, and Bas Spitters. "Bohrification of operator algebras and quantum logic." Synthese 186, no. 3 (2011): 719–52. http://dx.doi.org/10.1007/s11229-011-9918-4.

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21

FILIPPOV, A. T., A. P. ISAEV, and A. B. KURDIKOV. "PARAGRASSMANN ANALYSIS AND QUANTUM GROUPS." Modern Physics Letters A 07, no. 23 (1992): 2129–41. http://dx.doi.org/10.1142/s0217732392001877.

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Paragrassmann algebras with one and many paragrassmann variables are considered from the algebraic point of view without using the Green ansatz. A differential operator with respect to paragrassmann variable and a covariant para-super-derivative are introduced giving a natural generalization of the Grassmann calculus to a paragrassmann one. Deep relations between paragrassmann algebras and quantum groups with deformation parameters being root of unity are established.

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22

Meinrenken, Eckhard. "The Cubic Dirac Operator for Infinite-Dimensonal Lie Algebras." Canadian Journal of Mathematics 63, no. 6 (2011): 1364–87. http://dx.doi.org/10.4153/cjm-2011-036-9.

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AbstractLet be an infinite-dimensional graded Lie algebra, with dim , equipped with a non-degenerate symmetric bilinear form B of degree 0. The quantum Weil algebra is a completion of the tensor product of the enveloping and Clifford algebras of g. Provided that the Kac–Peterson class of g vanishes, one can construct a cubic Dirac operator D 2 , whose square is a quadratic Casimir element. We show that this condition holds for symmetrizable Kac– Moody algebras. Extending Kostant's arguments, one obtains generalized Weyl–Kac character formulas for suitable “equal rank” Lie subalgebras of Kac–Mo

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23

Daws, Matthew. "Quantum graphs: Different perspectives, homomorphisms and quantum automorphisms." Communications of the American Mathematical Society 4, no. 5 (2024): 117–81. http://dx.doi.org/10.1090/cams/30.

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We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional C ∗ C^* -algebras B B equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on L 2 ( B ) L^2(B) , the quantum adjacency matrices, or as certain operator bimodules over B ′ B’ . We present a simple, purely algebraic approach to proving equivalence between these settings, thus recovering existing results in the tracial state setting. For non-tracial states, our approach naturally suggests a generalisation of the operator bimodule definition, which takes a

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24

Van Den Bossche, Mathias, and Philippe Grangier. "Postulating the Unicity of the Macroscopic Physical World." Entropy 25, no. 12 (2023): 1600. http://dx.doi.org/10.3390/e25121600.

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We argue that a clear view of quantum mechanics is obtained by considering that the unicity of the macroscopic world is a fundamental postulate of physics, rather than an issue that must be mathematically justified or demonstrated. This postulate allows for a framework in which quantum mechanics can be constructed in a complete mathematically consistent way. This is made possible by using general operator algebras to extend the mathematical description of the physical world toward macroscopic systems. Such an approach goes beyond the usual type-I operator algebras used in standard textbook qua

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25

ZHAO, KAIMING. "WEYL TYPE ALGEBRAS FROM QUANTUM TORI." Communications in Contemporary Mathematics 08, no. 02 (2006): 135–65. http://dx.doi.org/10.1142/s0219199706002064.

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We introduce and study the quantum version of the differential operator algebra on Laurent polynomials and its associated Lie algebra over a field F of characteristic 0. The q-quantum torus Fq is the unital associative algebra over F generated by [Formula: see text] subject to the defining relations titj = qi,jtjti, where qi,i = 1, [Formula: see text]. Let D be a subspace of [Formula: see text] where ∂i is the derivation on Fq sending [Formula: see text] to [Formula: see text]. Then, the quantum differential operator algebra is the associative algebra Fq[D]. Assume that Fq[D] is simple as an a

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26

Kribs, David W., Comfort Mintah, Michael Nathanson, and Rajesh Pereira. "Operator and Graph Theoretic Techniques for Distinguishing Quantum States via One-Way LOCC." Applied Sciences 11, no. 20 (2021): 9542. http://dx.doi.org/10.3390/app11209542.

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We bring together in one place some of the main results and applications from our recent work on quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time to investigate the topic of distinguishability of sets of quantum states in quantum communication, with particular reference to the framework of one-way local quantum operations and classical communication (LOCC). We also derive a new graph-theoretic description of distinguishability in the case of a single-qubit sender.

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27

Ciaglia, Florio M., Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo, Luca Schiavone, and Alessandro Zampini. "Causality in Schwinger’s Picture of Quantum Mechanics." Entropy 24, no. 1 (2022): 75. http://dx.doi.org/10.3390/e24010075.

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This paper begins the study of the relation between causality and quantum mechanics, taking advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger’s picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. As a consequence of t

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28

CARIÑENA, JOSÉ F., JANUSZ GRABOWSKI, and GIUSEPPE MARMO. "QUANTUM BI-HAMILTONIAN SYSTEMS." International Journal of Modern Physics A 15, no. 30 (2000): 4797–810. http://dx.doi.org/10.1142/s0217751x00001956.

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We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the associative version of Nijenhuis tensors. Explicit examples, e.g. for the harmonic oscillator, are given.

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29

Eichenherr, H. "Minimal operator algebras in superconformal quantum field theory." Physics Letters B 151, no. 1 (1985): 26–30. http://dx.doi.org/10.1016/0370-2693(85)90817-2.

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30

Giuntini, Roberto, Antonio Ledda, and Francesco Paoli. "Expanding Quasi-MV Algebras by a Quantum Operator." Studia Logica 87, no. 1 (2007): 99–128. http://dx.doi.org/10.1007/s11225-007-9079-0.

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31

Schmidt, Simon, and Moritz Weber. "Quantum Symmetries of Graph C*-algebras." Canadian Mathematical Bulletin 61, no. 4 (2018): 848–64. http://dx.doi.org/10.4153/cmb-2017-075-4.

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AbstractThe study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have not yet been computed. We close this gap by proving that the quantum automorphism group of a finite, directed graph without multiple edges acts maximally on the corresponding graph C*-algebra. This shows that the quantum symmetry of a graph coincides with the quantum symmetry of the graph C*-algebra. In our result, we use the definition of quantum automorphism groups of graphs as given by Banica in 2005. Note that Bichon gave a different definition in 2003; our action is

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32

Bouchard, Vincent, Paweł Ciosmak, Leszek Hadasz, Kento Osuga, Błażej Ruba, and Piotr Sułkowski. "Super Quantum Airy Structures." Communications in Mathematical Physics 380, no. 1 (2020): 449–522. http://dx.doi.org/10.1007/s00220-020-03876-0.

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Abstract We introduce super quantum Airy structures, which provide a supersymmetric generalization of quantum Airy structures. We prove that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a supersymmetric generalization of the topological recursion. We reveal and discuss various properties of these supersymmetric structures, in particular their gauge transformations, classical limit, peculiar role of fermionic variables, and graphical representation of recursion relations. Furthermore, we present various examples of super quantum Airy struct

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33

Ahmad, H. A. S., H. Umair, M. S. Nurisya, and K. T. Chan. "Classical aspect of spin angular momentum in geometric quantum mechanics." Mathematical Modeling and Computing 12, no. 1 (2025): 49–56. https://doi.org/10.23939/mmc2025.01.049.

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Geometric Quantum Mechanics is a formulation demonstrating how quantum theory may be cast in the language of Hamiltonian phase-space dynamics. Within this framework, the classical properties of spin 1/2, spin 1 and spin 3/2 particles have been studied. The correspondence between the Poisson bracket and commutator algebras for these systems was shown by explicitly computing the value of the commutator of spin operators and comparing it with the Poisson bracket of the corresponding classical observables. This study was extended by comparing the Casimir operator and its classical counterpart. The

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34

Wetering, John van de. "An effect-theoretic reconstruction of quantum theory." Compositionality 1 (December 18, 2019): 1. http://dx.doi.org/10.32408/compositionality-1-1.

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An often used model for quantum theory is to associate to every physical system a C∗-algebra. From a physical point of view it is unclear why operator algebras would form a good description of nature. In this paper, we find a set of physically meaningful assumptions such that any physical theory satisfying these assumptions must embed into the category of finite-dimensional C∗-algebras. These assumptions were originally introduced in the setting of effectus theory, a categorical logical framework generalizing classical and quantum logic. As these assumptions have a physical interpretation, thi

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35

VASILIEV, M. A. "HIGHER SPIN ALGEBRAS AND QUANTIZATION ON THE SPHERE AND HYPERBOLOID." International Journal of Modern Physics A 06, no. 07 (1991): 1115–35. http://dx.doi.org/10.1142/s0217751x91000605.

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The oscillator-type realization is proposed for the continuous set of infinite-dimensional algebras of quantum operators on the two-dimensional sphere and hyperboloid. This realization is typical for infinite-dimensional higher spin algebras related to higher spin gauge theories. It involves the Klein-type operator that emerges nontrivially in the Heisenberg-type commutation relations for the oscillators. The invariant trace and bilinear form are constructed. The latter is shown to degenerate for all odd-integer values of the continuous parameter ν, which parametrizes the class of algebras und

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ÖZER, H. T. "ON THE SUPER FIELD REALIZATION OF SUPER-CASIMIR ${\mathcal W} {\mathcal A} _n$ ALGEBRAS." International Journal of Modern Physics A 17, no. 03 (2002): 317–25. http://dx.doi.org/10.1142/s0217751x02005980.

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We give an explicit quantum super field construction of the [Formula: see text] super-Casimir [Formula: see text] algebras, which is obtained from supersymmetric Miura transformation for the Lie super-algebra [Formula: see text]. And also we give an extension of this algebras including a super-vertex operator which depends on simple root system of [Formula: see text].

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37

Novikov, S. P. "Various doublings of Hopf algebras. Operator algebras on quantum groups, complex cobordisms." Russian Mathematical Surveys 47, no. 5 (1992): 198–99. http://dx.doi.org/10.1070/rm1992v047n05abeh000957.

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38

Müger, Michael. "Quantum Double Actions on Operator Algebras and Orbifold Quantum Field Theories." Communications in Mathematical Physics 191, no. 1 (1998): 137–81. http://dx.doi.org/10.1007/s002200050264.

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Sasaki, Ryu. "Exactly and quasi-exactly solvable ‘discrete’ quantum mechanics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1939 (2011): 1301–18. http://dx.doi.org/10.1098/rsta.2010.0262.

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A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q -oscillator algebra and the Askey–Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional ‘discrete’ quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric ort

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40

ACCARDI, LUIGI, and ANILESH MOHARI. "TIME REFLECTED MARKOV PROCESSES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 02, no. 03 (1999): 397–425. http://dx.doi.org/10.1142/s0219025799000230.

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A classical stochastic process which is Markovian for its past filtration is also Markovian for its future filtration. We show with a counterexample based on quantum liftings of a finite state classical Markov chain that this property cannot hold in the category of expected Markov processes. Using a duality theory for von Neumann algebras with weights, developed by Petz on the basis of previous results by Groh and Kümmerer, we show that a quantum version of this symmetry can be established in the category of weak Markov processes in the sense of Bhat and Parthasarathy. Here time reversal is im

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41

Ozawa, Narutaka, and Marc A. Rieffel. "Hyperbolic Group C*-Algebras and Free-Product C*-Algebras as Compact Quantum Metric Spaces." Canadian Journal of Mathematics 57, no. 5 (2005): 1056–79. http://dx.doi.org/10.4153/cjm-2005-040-0.

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AbstractLet ℓ be a length function on a group G, and let Mℓ denote the operator of pointwise multiplication by ℓ on ℓ2(G). Following Connes, Mℓ can be used as a “Dirac” operator for C*r(G). It defines a Lipschitz seminorm on C*r(G), which defines a metric on the state space of C*r(G). We show that if G is a hyperbolic group and if ℓ is a word-length function on G, then the topology from this metric coincides with the weak-* topology (our definition of a “compact quantum metric space”). We show that a convenient framework is that of filtered C*-algebras which satisfy a suitable “Haagerup-type”

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Kümmerer, Burkhard, and Kay Schwieger. "Diagonal couplings of quantum Markov chains." Infinite Dimensional Analysis, Quantum Probability and Related Topics 19, no. 02 (2016): 1650012. http://dx.doi.org/10.1142/s0219025716500120.

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In this paper we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by analyzing couplings. For a given tensor dilation we construct a self-coupling of a Markov operator. It turns out that the coupling is a dual version of the extended dual transition operator studied by Gohm et al. We deduce that this coupling is successful if and only if the dilation is asymptotically complete.

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43

Cho, Kenta. "Semantics for a Quantum Programming Language by Operator Algebras." Electronic Proceedings in Theoretical Computer Science 172 (December 28, 2014): 165–90. http://dx.doi.org/10.4204/eptcs.172.12.

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44

Kuramochi, Yui. "Quantum incompatibility of channels with general outcome operator algebras." Journal of Mathematical Physics 59, no. 4 (2018): 042203. http://dx.doi.org/10.1063/1.5008300.

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45

Wang, Shuzhou. "Ergodic Actions of Universal Quantum Groups on Operator Algebras." Communications in Mathematical Physics 203, no. 2 (1999): 481–98. http://dx.doi.org/10.1007/s002200050622.

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De Sole, Alberto, Victor G. Kac, and Daniele Valeri. "A Lax type operator for quantum finite W-algebras." Selecta Mathematica 24, no. 5 (2018): 4617–57. http://dx.doi.org/10.1007/s00029-018-0439-6.

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Cho, Kenta. "Semantics for a Quantum Programming Language by Operator Algebras." New Generation Computing 34, no. 1-2 (2016): 25–68. http://dx.doi.org/10.1007/s00354-016-0204-3.

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Klevtsov, S. E. "Toward a vertex operator construction of quantum affine algebras." Theoretical and Mathematical Physics 154, no. 2 (2008): 201–8. http://dx.doi.org/10.1007/s11232-008-0019-6.

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Yan, Jun, and Shi-Ke Hu. "The q -Analogous Vertex Operator and Quantum Affine Algebras." Communications in Theoretical Physics 19, no. 4 (1993): 505–8. http://dx.doi.org/10.1088/0253-6102/19/4/505.

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Brannan, Michael. "Reduced operator algebras of trace-preserving quantum automorphism groups." Documenta Mathematica 18 (2013): 1349–402. http://dx.doi.org/10.4171/dm/430.

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