August 2015
Beginner
270 pages
8h 21m
English
Content preview from Introduction to Quantum Physics and Information Processing
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38 Introduction to Quantum Physics and Information Processing
by dividing it by its norm:
|vi
norm
=
|vi
kvk
.
• Orthogonality: vectors |ψi and |φi are orthogonal to each other iff
hψ|φi = 0.
A Hilbert space spanned by n linearly independent vectors |ii, i = 1...n is
said to be n-dimensional. The set then defines a basis for the space. A generic
vector in the space can be expressed as a linear combination of these basis
states with complex coefficients c
i
:
|ψi =
n
X
i=1
c
i
|ii. (3.2)
In matrix representation, the natural basis vectors are the n-column vectors
|0i =
1
0
.
.
.
0
; |1i =
0
1
.
.
.
0
; ... |ni =
0
0
.
.
.
1
.
It is useful to note that the ...
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