Alice and Bob in Quantum Wonderland

Alice and Bob in the
Quantum Wonderland
Two Easy Sums
7873 x 6761
=
?
=
x
?
?
26 292 671
Superposition
The mystery of
+
How can a particle be a wave?
Polarisation
Three obstacles are easier than two
Addition of polarised light
=
+
=
+

The individual photon
PREPARATION
MEASUREMENT
Yes
No
How it looks to the photon in the stream (2)
PREPARATION
MEASUREMENT
MAYBE!
States of being
=
|NE 
+
|N 
=
|N 
|E
+
|NE 
|NW
Quantum addition
+
=
+
Alive
+
Dead
=
= ?
Schrödinger’s Cat
|CAT = |ALIVE + |DEAD
Entanglement
+
Observing
either side
breaks the
entanglement
Entanglement killed the cat
+
According to quantum theory, if a cat can be in a state
|ALIVE  and a state |DEAD, it can also be in a state
|ALIVE + |DEAD.
Why don’t we see cats in such
superposition states?
Entanglement killed the cat
ANSWER: because the theory actually predicts…..
[
[
+
]+[
]
??
?
]
Entangled every which way
+
=
+
Einstein-Podolsky-Rosen argument
If one photon passes through the polaroid, so
does the other one.
Therefore each photon must already have
instructions on what to do at the polaroid.
The no-signalling theorem
I know what message
Bob is getting right now
But I can’t make
it be my message!
Quantum entanglement can
never be used to send
information that could not be
sent by conventional means.
Quantum cryptography
0
0
1
1
0
0
0
0
1
1
Alice and Bob now share a
secret key which didn’t exist
until they were ready to use it.
Quantum information
Yes
θ
No
1 qubit
Θ=0.0110110001…
To calculate the behaviour of a
photon, infinitely many bits of
information are required
1 bit
0 or 1
– but only one bit can be extracted.
Yet a photon does this calculation!
Available information: one qubit
1 qubit
0
1 bit
1
or
x
1 qubit
1 bit
y
Available information: two qubits
0 0
+
W
0 1
-
X
1 0
+
Y
1 1
-
Z
2 qubits  2 bits
or
2 qubits  2 bits
Teleportation
Measurement
Transmission
?
Reception
Reconstruction
Quantum Teleportation
Measure
W,X,Y,Z?
Dan Dare, Pilot of the Future. Frank Hampson, Eagle (1950)
Dan Dare, Pilot of the Future. Frank Hampson, Eagle (1950)
Nature 362, 586-587
(15 Apr 1993)
Computing
INPUT
N digits
COMPUTATION
Running time T
OUTPUT
How fast does T grow as you increase N?
Quantum Computing
6+4
+
20/3
+
100
In 1 unit of time, many calculations can be done
but only one answer can be seen
But you can choose your question
E.g. Are all the answers the same?
Two Easy Sums
7873 x 6761
=
53 229
? 353
?
=
26 292 671
x
?
Not so easy
N
T for
multiplying
two N-digits
T for factorising a
2N-digit number
1
1
2
2
4
4
3
9
8
4
16
16
5
25
32
10
100
1,024
20
400
1,048,576
30
900
1,073,741,824
40
1600
1,099,511,627,776
50
2500
1,125,899,906,842,620
T≈N2
T≈2N
But on a quantum
computer,
factorisation can be
done in roughly the
same time as
multiplication
.
T≈N2
(Peter Shor, 1994)
Key Grip
Visual Effects
Focus Puller
Lieven Clarisse
Bill Hall
Paul Butterley
NoBest
cats
the
Boywere harmed
Jeremyin
Coe
preparation of this lecture
Alice
Bob
Sarah Page
Tim Olive-Besly

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