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Beyond stabilizer codes II: Clifford codes 总被引:1,自引:0,他引:1
Klappenecker A. Rotteler M. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2002,48(8):2396-2399
For pt. I see ibid., vol.48, no.8, p.2392-95 (2002). Knill (1996) introduced a generalization of stabilizer codes, called Clifford codes. It remained unclear whether or not Clifford codes can be superior to stabilizer codes. We show that Clifford codes are stabilizer codes provided that the abstract error group has an Abelian index group. In particular, if the errors are modeled by tensor products of Pauli matrices, then the associated Clifford codes are necessarily stabilizer codes. 相似文献
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Salah A. Aly Andreas Klappenecker Pradeep Kiran Sarvepalli 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2007,53(3):1183-1188
Classical Bose-Chaudhuri-Hocquenghem (BCH) codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its dual code only if its designed distance delta=O(radicn), and the converse is proved in the case of narrow-sense codes. Furthermore, the dimension of narrow-sense BCH codes with small design distance is completely determined, and - consequently - the bounds on their minimum distance are improved. These results make it possible to determine the parameters of quantum BCH codes in terms of their design parameters 相似文献
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Klappenecker A. Rotteler M. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2005,51(3):1084-1089
Unitary error bases generalize the Pauli matrices to higher dimensional systems. Two basic constructions of unitary error bases are known: An algebraic construction by Knill that yields nice error bases, and a combinatorial construction by Werner that yields shift-and-multiply bases. An open problem posed by Schlingemann and Werner relates these two constructions and asks whether each nice error basis is equivalent to a shift-and-multiply basis. We solve this problem and show that the answer is negative. However, we find that nice error bases have more structure than one can anticipate from their definition. In particular, we show that nice error bases can be written in a form in which at least half of the matrix entries are 0. 相似文献
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We show how randomized caches can be used in resource-poor partial-state routers to provide a fair share of bandwidth to short-lived flows that are known as mice when long-lived flows known as elephants are present. 相似文献
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A method to compute the discrete wavelet transform for certain wavelet filters is proposed that takes advantage of conjugacy properties in number fields. It is shown that wavelet filters derived from compactly supported orthonormal wavelets can be approximated with arbitrary precision by the proposed wavelet filters. © 1996 John Wiley & Sons, Inc. 相似文献
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Beyond stabilizer codes .I. Nice error bases 总被引:2,自引:0,他引:2
Klappenecker A.A. Rotteler M. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2002,48(8):2392-2395
Nice error bases have been introduced by Knill (1996) as a generalization of the Pauli basis. These bases are shown to be projective representations of finite groups. We classify all nice error bases of small degree, and all nice error bases with Abelian index groups. We show that, in general, an index group of a nice error basis is necessarily solvable. 相似文献
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