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Dual Density Operators and Natural Language
Dual Density Operators and Natural Language

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Classical phase-space analysis of vibronically coupled systems

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... “enough” precision, to control its interaction with other qubits, and to do so during a time interval “much shorter” than the decoherence time. 1.5 Qubit-specific measurement capability. Theoretically, we should be able to measure the state of each qubit independently of any other parameters of the ...
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Chapter 5 Quantum Information Theory

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Hubbard model description of silicon spin qubits: charge stability

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Nature’s Queer Performativity “O 25

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Semi-classical formula beyond the Ehrenfest time in

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Continuous Variable Quantum Information: Gaussian States and

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Quantum group

In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra. There is no single, all-encompassing definition, but instead a family of broadly similar objects.The term ""quantum group"" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a `bicrossproduct' class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo.In Drinfeld's approach, quantum groups arise as Hopf algebras depending on an auxiliary parameter q or h, which become universal enveloping algebras of a certain Lie algebra, frequently semisimple or affine, when q = 1 or h = 0. Closely related are certain dual objects, also Hopf algebras and also called quantum groups, deforming the algebra of functions on the corresponding semisimple algebraic group or a compact Lie group.Just as groups often appear as symmetries, quantum groups act on many other mathematical objects and it has become fashionable to introduce the adjective quantum in such cases; for example there are quantum planes and quantum Grassmannians.
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