Ph219a/CS219a
Solutions
Nov 8, 2013
Problem 2.1
(a) Consider how the protocol works for the special case n = 1, ie. when Alice encrypts a single
qubit state . The eect of Alices encryption protocol ca
1
Ph 219a/CS 219a
Exercises
Due: Wednesday 23 October 2013
1.1 How far apart are two quantum states?
Consider two quantum states described by density operators and
in an N -dimensional Hilbert space,
1
Ph 219b/CS 219b
Exercises
Due: Wednesday 4 December 2013
4.1 The peak in the Fourier transform
In the period nding algorithm we prepared the periodic state
1
A
A1
j=0
|x0 + jr ,
(1)
where A is the l
Ph219a/CS219a
Solutions to Hw 4
December 2013
Problem 4.1
(a) Simple trigonometry tells us
Prob(y) =
sin2 Ar
sin2 r
1
NA
1
NA
1
sin r
(1)
2
Further, note that1
sin x
2
x
sin2 x
x2
]
2
4
, x [
, ]
2
Ph219a/CS219a
Solutions
Nov 8, 2013
Problem 1.1
(a) Since pa = Tr(Ea ) and pa = Tr(Ea ),
N
1
1
|pa pa | = |Tr( ( )Ea )|
2 a=1
2
d(p, p) =
Writing in its eigen-basis, we have =
i
(1)
i |i i|, so that
N
Ph219a/CS219a
Solutions of Problem Set 7
March 18, 2009
Problem 1
(a) Clearly for x = 1, lnx = x 1 = 0. Since the function f (x) = lnx is strictly concave,
lnx x 1 for x = 1, if x 1 is a tangent at x
Ph219a/CS219a
Solutions of Problem Set 6
March 16, 2014
Problem 1
(a) We can write Xa as a product of X s and Z s:
n
n
Xa = (sgn)
u
X
=1
v
Z , u , v cfw_0, 1
(1)
=1
Then, XA,a XB,a can be written as
Ph219a/CS219a
Solutions
Nov 8, 2013
Problem 3.1
(a) Constructing the unitary transformation U1 as given in the circuit, we have U1 = (H
I)(P)(H I). In the standard basis, H and P are given by
1
H=
2
1
Ph 219b/CS 219b
Exercises
Due: Wednesday 20 November 2013
3.1 Universal quantum gates I
In this exercise and the two that follow, we will establish that several
simple sets of gates are universal fo
1
Ph 219a/CS 219a
Exercises
Due: Wednesday 6 November 2013
2.1 The price of quantum state encryption
Alice and Bob are working on a top secret project. I cant tell you
exactly what the project is, but
Ph219a/CS219a
Solutions 5
Feb 5, 2014
Problem 5.1
(a) The derivation of the Gilbert-Varshamov (GV) bound for CSS codes follows closely the
argument discussed in class for the general GV bound, except