Alice and Bob in the Quantum Wonderland

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Alice and Bob in theQuantum Wonderland
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Two Easy Sums

• 7873 x 6761 ?
• ? x ? 26 292 671

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Superposition

• The mystery of

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(No Transcript)
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How can a particle be a wave?
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Polarisation
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Three obstacles are easier than two
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Addition of polarised light
?






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The individual photon
PREPARATION
MEASUREMENT
Yes
No
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How it looks to the photon in the stream (2)
PREPARATION
MEASUREMENT
MAYBE!
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States of being
E?
NE ?
N ?
NW?
N ?
NE ?
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Quantum addition




Alive Dead ?

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Schrödingers Cat
CAT? ALIVE? DEAD?
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Entanglement

Observing either side breaks the entanglement
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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 stateALIVE? DEAD?.
Why dont we see cats in such superposition
states?
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Entanglement killed the cat
ANSWER because the theory actually predicts..
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Entangled every which way



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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.
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(No Transcript)
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The no-signalling theorem
I know what message Bob is getting right now
Quantum entanglement can never be used to send
information that could not be sent by
conventional means.
But I cant make it be my message!
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Quantum cryptography
0
0
1
1
0
0
0
0
1
1
Alice and Bob now share a secret key which
didnt exist until they were ready to use it.
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Quantum information
Yes
?
No
1 qubit T0.0110110001
1 bit 0 or 1
To calculate the behaviour of a photon,
infinitely many bits of information are required
but only one bit can be extracted.
Yet a photon does this calculation!
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Available information one qubit
0
1 qubit
1 bit
1
or
x
1 qubit
1 bit
y
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Available information two qubits
0 0
0 1
1 0
1 1
2 qubits ? 2 bits
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Teleportation
Transmission
Reception
Measurement
Reconstruction
?
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Quantum Teleportation
Measure
W,X,Y,Z?
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Dan Dare, Pilot of the Future. Frank Hampson,
Eagle (1950)
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Dan Dare, Pilot of the Future. Frank Hampson,
Eagle (1950)
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Nature 362, 586-587 (15 Apr 1993)
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Computing
INPUT N digits
COMPUTATION Running time T
OUTPUT
How fast does T grow as you increase N?
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Quantum Computing
64
20/3
But you can choose your question
E.g. Are all the answers the same?
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Two Easy Sums

• 7873 x 6761 ?
• ? x ? 26 292 671

53 229 353
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Not so easy .
But on a quantum computer, factorisation can be
done in roughly the same time as multiplication
T N 2 (Peter Shor, 1994)
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 N 2 T 2 N
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Key Grip Lieven
Clarisse Visual Effects
Bill Hall Focus Puller Paul
Butterley Best Boy Jeremy
Coe
No cats were harmed in the preparation of this
lecture
Alice Sarah
Page Bob Tim
Olive-Besly