NDLI: Nice nearrings

Content Provider	IEEE Xplore Digital Library
Author	Klappenecker, A.
Copyright Year	2012
Description	Author affiliation: Department of Computer Science and Engineering, Texas A&M University, College Station, TX 77843-3112, USA (Klappenecker, A.)
Abstract	Nice error bases are a fundamental primitive of quantum information processing. For example, they govern the discretization of errors in quantum error-correcting codes. It is show that the generalized Pauli basis, the most widely used example of nice error bases, has some remarkable structural properties. However, the generalized Pauli basis is limited to dimensions that are a power of a prime, since it is constructed with the help of a finite field. A wider class of nice error bases is introduced that shares many features of the generalized Pauli basis, yet allows one to remove the restriction to prime power dimensions. The nice error bases are indexed by nearrings. Nearrings that support the construction of nice error bases are called nice. It is shown that all finite nearfields are nice. It is shown that a finite ring is nice if and only if it finite Frobenius ring. Several fundamental properties of nice nearrings are established.
Starting Page	170
Ending Page	173
File Size	96421
Page Count	4
File Format	PDF
ISBN	9781467325806
ISSN	21578117
e-ISBN	9781467325790
e-ISBN	9781467325783
DOI	10.1109/ISIT.2012.6283569
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-07-01
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Additives Error correction codes Indexes Vectors Kernel Educational institutions
Content Type	Text
Resource Type	Article

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