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Improved Quantum Metrology Using Quantum Error Correction
Improved Quantum Metrology Using Quantum Error Correction

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... a proof for the randomized one-way communication complexity of HMn . We also show that our lower√bound is tight by describing a randomized√one-way protocol with communication O( n). In this protocol, Alice just sends O( n) random bits of her input. By the birthday paradox, with high probability, Bob ...
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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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