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Entanglement – Beamen – Quantum
cryptography
The weird quantum world
Bernd Hüttner CPhys FInstP
DLR Stuttgart
Institute of Technical Physics
Quantum mechanics
… is strange!
 Particles behave like waves
 Particles can be simultaneously
in two states
 Quanten cannot be cloned
 Entangled particles are correlated to all times
at arbitrarily distances
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Double-slit experiment
Richard Feynman:
„Wave particle dual behavior
contains the basic mystery of
quantum mechanics. In reality it
contains the only mystery.
Complementarity: Which way versus interference
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1
 
  1    2
2
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
1 2
       1 1   2  2  2 
2
1
  *  2 1  * 1  2 
2
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Double-slit experiment with Fullerenes
Diameter:
C60  1
nm
dB  3 pm
C60
Laser
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Feynman:
Regardless of the quantum system,
any information – recorded or not –
about the alternative taken by a
quantum process capable of following
more than one alternative destroys the
interference between alternatives.
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Quotes to ponder …
Niels Bohr:
“Anyone who is not shocked by quantum theory has
not understood it.”
Richard Feynman:
“… I think I can safely say that nobody understands
quantum mechanics.”
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Entanglement - Verschränkung
Entanglement is the characteristic trait of quantum mechanics, the
one that enforces its entire departure from classical lines of thought
Independent on the basis
Independent on the distance
Leads to strong correlations – stronger than in classical physics
Demonstrates the differences between quantum and classical
physics in the most drastical way
Entanglement and Bell‘s inequality test hidden variables theories
Reveals nonlocality – a classical theory of the world is impossible
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What is entanglement really?
Einstein: „Spooky action on a distance“
If a quantum system consists of more than one particle (photon, atom…) then
superposition leads to an entangled, non separable state.
Example: Polarisation |H> und |V> → Superposition:  = 1/√2 {|H> +
|V>}
2 Photons: possible polarizations: |H>1, |H>2 und |V>1, |V>2
Superposition:
|   
1
| H 1 | H  2  | V 1 | V  2 
2
Measurement of only 1 photon gives with P=0.5 |H> or |V> (complete uncertainty)
measurement of both photons results in perfect correlations.
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Production of entangled
photons
More exactly: polarizations are each other perpendicular
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Bell‘s inequality
Henry R. Stapp (Berkeley) called Bell‘s theorem
„the most profound discovery of science“!
BI provides value for the correlation S of 2 simultaneously produced particles
SHVT local realism)
SQM > 2 (nonlocal)
That means, measurement on particle 1 forces immediately the property of
particle 2 in any distance! No contradiction to theory of relativity.
Quantum theory is not understandable - but right!
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Violation of Bell‘s inequality
experimental results
|S|
QM
LR
Voltage (~Winkel)
GHZ-states: SHVT = 1
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SQM = Sexp = -1
Beamen
Quantum teleportation
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 Bob and Alice create photons
 Can’t just measure one and copy it
 So Alice makes EPR pair, send one photon to Bob
 Lets own photon interact with EPR photon (Bell measurement) records outcome - destroys own photon
 Instantaneously changes state of Bob’s EPR Photon
 Send Bob outcome of Alice’s observations of interaction
 Bob uses observations to adjust EPR photon to interact with own
photon to make own photon copy of Alice’s
Note, not the object (photon) is teleported but just its state.
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TELEPORTATION
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Bell states
Cryptography - One-Time-Pad
plain text: 4 2 3 7 1 5 0
binär:
key:
1111010111001010000001
(22 Bit)
1010110100100010101011
(22 Bit)
XOR operation
Cipher:
0101100011101000101010
(22 Bit)
XOR operation
plain
text:
1111010111001010000001
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(22 Bit)
Guessing the Secret Key
Key Size Number
(bits)
Of Keys
Time at Time at
1 µs each 1 ps each
32
4.3x109
35.8 min
2.15 ms
56
7.2x1016
1142 yr
10 hr
128
3.4x1038
5.4x1024 yr 5.4x1018 yr
168
3.7x1050
5.9x1036 yr 5.9x1030 yr
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Quantum computer versus digital computer
Net work of 100 computers
Number of N
Calculation time
1024bit
100 000 years
4096bit
over 30 billion years
Quantum computer with 100MHz
Number of N
Calculation time
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1024bit
4.5 minutes
4096bit
4.8 hours
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Quantum cryptography or better
quantum key distribution
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Detect if someone is listening
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Example
Alice's Key
Original: (a)
Encrypted: (b)
Bitwise
XOR
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Bob's Key
Decrypted: (c)
Bitwise
XOR
DARPA Quantum Network
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Interaction-free measurement
Elitzur, Vaidman (1993), Kwiat et al. (1995)
D
D
Ifm
Ifm
D
D
Bomb
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Summary and outlook
Why is this so very
important?
We are in the age of quantum information processing
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Gordon Moore, 1965: “Every 18 months microprocessors double in speed.”
Quantum computing
Quantum communication
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Quantum teleportation
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