hw07soln - May 5, 2005 Physics 681-481; CS 483: Discussion...

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: May 5, 2005 Physics 681-481; CS 483: Discussion of #7 1. (a) If only one-qubit bit-flip errors are allowed, then the general corruption of an n-qubit code word | Ψ i is of the form ( | d i 1 + n X i =1 | a i i X i ) | Ψ i . (1) We need 2( n +1) dimensions to accomodate each of the n +1 terms in (1) in orthogonal two- dimensional subspaces, and an n-qubit code word provides 2 n dimensions. We therefore require 2 n ≥ 2 n + 2 . (2) The smallest n satisfying this condition is n = 3, for which it holds as an equality. (b) Take the two three-qubit codewords to be | i = | 000 i , | 1 i = | 111 i . (3) The two operators Z 1 Z 2 and Z 2 Z 3 (4) commute with each other and act as the identity on both code words (3). X 1 commutes with the second and anticommutes with the first; X 3 commutes with the first and anticommutes with the second; and X 2 anticommutes with both. So measuring both of the operators (4) projects the corrupted state (1) onto one of the four terms with a pattern of eigenvalues...
View Full Document

This note was uploaded on 09/28/2008 for the course PHYS 481 taught by Professor Anon during the Spring '05 term at Cornell University (Engineering School).

Page1 / 3

hw07soln - May 5, 2005 Physics 681-481; CS 483: Discussion...

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