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A perfect code may be interpreted as one in which the balls of Hamming radius t centered on codewords exactly fill out the space (t is the covering radius = packing radius). A quasi-perfect code is one in which the balls of Hamming radius t centered on codewords are disjoint and the balls of radius t+1 cover the space, possibly with some ...
In quantum information theory, a set of bases in Hilbert space C d are said to be mutually unbiased if when a system is prepared in an eigenstate of one of the bases, then all outcomes of the measurement with respect to the other basis are predicted to occur with an equal probability inexorably equal to 1/d.
The first error-correcting code was the Hamming(7,4) code, developed by Richard W. Hamming in 1950. This code transforms a message consisting of 4 bits into a codeword of 7 bits by adding 3 parity bits.
In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code with block length , size and minimum distance . It is also known as the Joshibound [ 1 ] proved by Joshi (1958) and even earlier by Komamiya (1953) .
That these codes allow indeed for quantum computations of arbitrary length is the content of the quantum threshold theorem, found by Michael Ben-Or and Dorit Aharonov, which asserts that you can correct for all errors if you concatenate quantum codes such as the CSS codes—i.e. re-encode each logical qubit by the same code again, and so on, on ...
2.3 Quantum uncertainty. 2.4 Angular momentum. 2.5 Hydrogen atom. 3 See also. 4 Footnotes. 5 Sources. ... so that it has either a finite L 2-norm (if it is a bound ...
The quantum information-theoretic interpretation of the above inequality is that the probability of obtaining outcome from a quantum measurement acting on the state is upper bounded by the probability of obtaining outcome on the state summed with the distinguishability of the two states and .
Performance of CIRC: [7] CIRC conceals long bust errors by simple linear interpolation. 2.5 mm of track length (4000 bits) is the maximum completely correctable burst length. 7.7 mm track length (12,300 bits) is the maximum burst length that can be interpolated.