Download - Alice and Bob in the Quantum Wonderland
How it looks to the photon in the How it looks to the photon in the stream (2)stream (2)
MEASUREMENTMEASUREMENTPREPARATIONPREPARATION
MAYBEMAYBE!!
EntanglementEntanglement
Observing Observing either side either side breaks the breaks the entanglemeentangleme
ntnt
++
Entanglement killed the catEntanglement killed the cat
According to quantum theory, if a cat can be in According to quantum theory, if a cat can be in
a state |ALIVE a state |ALIVE and a state |DEAD and a state |DEAD, it can also , it can also
be in a statebe in a state
|ALIVE|ALIVE + |DEAD + |DEAD..
Why don’t we see cats in Why don’t we see cats in such superposition statessuch superposition states??
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Entanglement killed the catEntanglement killed the cat
++
ANSWER: because the theory actually ANSWER: because the theory actually predicts…..predicts…..
[[ ++]] ]][[
[[ ]]?
??
Einstein-Podolsky-Rosen Einstein-Podolsky-Rosen argumentargument
If one photon passes through the If one photon passes through the polaroid, so does the other one.polaroid, so does the other one.
Therefore each photon must already Therefore each photon must already have instructions on what to do at have instructions on what to do at
the polaroid.the polaroid.
The no-signalling theoremThe no-signalling theorem
I know what message Bob is
getting right nowQuantum entanglement
can never be used to send information that could not be sent by conventional means.
But I can’t make it be
my message!
Quantum cryptographyQuantum cryptography
0
1
0
0
1
0
1
0
0
1Alice and Bob now share a secret key which didn’t exist
until they were ready to use it.
Quantum informationQuantum information
θ
1 qubitΘ=0.0110110001
…
Yet a photon does this calculation!
1 bit0 or 1
YesYes
NoNo
To calculate the behaviour of a photon, infinitely many bits of
information are required
– but only one bit can be extracted.
Available information: one Available information: one qubitqubit
1 qubit
1
0
1 qubit
1 bit
y
x
1 bit
or
Available information: two Available information: two qubitsqubits
0 0
1 0
1 1
0 1
2 qubits 2 bits 2 qubits 2 bits
+
-
+
-
W
Z
Y
X
or
ComputingComputing
INPUTN digits
COMPUTATIONRunning time T
OUTPUT
How fast does T grow as you increase N?
Quantum ComputingQuantum Computing
But you can choose your question
++ ++
In 1 unit of time, many calculations can be done but only one answer can be seen
E.g. Are all the answers the same?
6+4 20/3 100
Two Easy SumsTwo Easy Sums
7873 x 6761 = ?7873 x 6761 = ?
? x ? = 26 292 671? x ? = 26 292 671
53 229 353
Not so easy Not so easy ..
N
T for multiplying
two N-digitsT 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
But on a quantum computer,
factorisation can be done in roughly the
same time as multiplication
T ≈ N 2
(Peter Shor, 1994)
No cats were harmed in the No cats were harmed in the preparation of this lecturepreparation of this lecture
Key Grip Lieven ClarisseKey Grip Lieven Clarisse
Visual Effects Bill HallVisual Effects Bill Hall
Focus Puller Paul ButterleyFocus Puller Paul Butterley
Best Boy Jeremy CoeBest Boy Jeremy Coe
Alice Sarah Alice Sarah PagePage
Bob Tim Olive-Bob Tim Olive-BeslyBesly