Classical information can be duplicated, while quantum informationcannot , .It is well known that classical information can be protected from degradation by the use ofclassical error-correcting codes . M. Since the discussion in  was necessarily very condensed, we give the proof of thistheorem below.Theorem 1. Your cache administrator is webmaster. http://caribtechsxm.com/quantum-error/quantum-error-correction-codes.php
Classical inform ation cannot travel faster than light, while quan-tum in formation appears to in some circumstances (although proper deﬁnitions can resolvethis apparent paradox). Rains P. Institutional Sign In By Topic Aerospace Bioengineering Communication, Networking & Broadcasting Components, Circuits, Devices & Systems Computing & Processing Engineered Materials, Dielectrics & Plasmas Engineering Profession Fields, Waves & Electromagnetics General Use of this web site signifies your agreement to the terms and conditions. https://arxiv.org/abs/quant-ph/9608006
The resulting pairs can then beused to teleport quantum information from one experimenter to the other . A. Inform. Copyright © 2016 ACM, Inc.
Schlingemann, R.F. Section 3 shows that these spaces in turn areequivalent to a certain class of additive codes over GF (4) (Theorem 2). An additive quantum-error-correcting code Q with associated space¯S can correcta set of errors Σ ⊆ E prec i sely when ¯e−11¯e26∈¯S⊥\¯S for all e1, e2∈ Σ.Proof. J.
Shor N. The distance between two elements (a|b), (a′|b′) ∈¯E is deﬁned tobe the weight of their diﬀerence.Then we have the followin g theorem, which is an immediate consequence of Theorem 1of . Rains , P. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.5670 The dimension of a totally isotropic su b space is at most n.
Alternatively stated, they are a small section of the system Hilbert space where the system is decoupled from the environment and thus its evolution is completely unitary. Rains3rd P.M. Rains, P.M. Kim, V.
It is also the group generated by fault-tolerant bitwise operations performed on qubits that are encoded by certain quantum codes , , . http://caribtechsxm.com/quantum-error/quantum-computation-quantum-error-correcting-codes-and-information-theory.php J. Huffman, J.-L. W.
Inthe present paper we develop the theory to the point where it is possible to apply standardtechniques f rom classical coding theory to construct quantum codes. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, coding theory and Quantum error correction. Use of this web site signifies your agreement to the terms and conditions. http://caribtechsxm.com/quantum-error/quantum-error-correction-with-degenerate-codes-for-correlated-noise.php This induces a decom-position of2ninto orthogonal eigenspaces.
We have now completed the proof ofTheorem1: Q maps k qubits into n qubits and can correct [(d −1)/2] errors.Deco ding. Gaborit On extremal additive F4 codes of length 10 to 18 J. Inform.
To determine which eigenspace contains a given state it is thereforeenough to determine this character. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubitsDiscover the world's research11+ million Sloane, S. Of course, an [[n, k, d]] code is also an ((n, 2k, d)) code.Readers who are most interested in the codes themselves could now proceed directly toSection 3.Proof.
Replaced Sept. 24, 1996, to correct a number of minor errors. Inner products allow the rigorous introduction of intuitive geometrical notions such as the length of a vector or the angle between two vectors. The term lower bound is defined dually as an element of P which is less than or equal to every element of S. click site Generated Tue, 25 Oct 2016 02:48:27 GMT by s_wx1157 (squid/3.5.20)
Of course, as in classical coding theory,identifying the most likely error given the synd rome can be a diﬃcult problem. (There is notheoretical diﬃculty, since in p rinciple an exhaustive search