assignment7 - April 20, 2006 Physics 681-481; CS 483:...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: April 20, 2006 Physics 681-481; CS 483: Assignment #7 (please hand in after the lecture, Thursday, May 4) This is the final assignment. 1. Suppose the only kinds of errors one had to worry about were bit-flip errors, but one wanted to take into account not only single bit-flips ( X i ) in the code words but also double bit-flips ( X i X j , i 6 = j ). (a) Show that there is an n for which the dimension of the n-Qbit state space is just large enough to accomodate mutually orthogonal two-dimensional subspaces for the uncor- rupted code words and all code words suffering either single or double bit-flip corruptions. What is that n ? (b) Show for the n you found in (a) that there is indeed a perfect n-Qbit code that corrects all single and double bit-flip errors, by writing down the states that encode | i and | 1 i , and writing down a set of commuting hermitian operators whose squares are unity, that preserve both codewords, and have distinct patterns of commutations or anticommutations (show this explicitly) with each of the operators associated with all the single and double...
View Full Document

This homework help was uploaded on 02/01/2008 for the course CS 483 taught by Professor Ginsparg during the Spring '08 term at Cornell University (Engineering School).

Page1 / 3

assignment7 - April 20, 2006 Physics 681-481; CS 483:...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online