institute of technical physics entanglement – beamen – quantum cryptography the weird quantum...
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Institute of Technical Physics
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
Institute of Technical Physics
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
Institute of Technical Physics
Institute of Technical Physics
1 2
1
2
2 21 1 2 2
* *2 1 1 2
1
21
2
Institute of Technical Physics
Institute of Technical Physics
Double-slit experiment with Fullerenes
C 60
Diameter:C60 1 nm
dB 3 pm
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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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.”
Quotes to ponder …
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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
Entanglement - VerschränkungEntanglement - Verschränkung
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What is entanglement really?
If a quantum system consists of more than one particle (photon, atom…) then superposition leads to an entangled, non separable state.
Einstein: „Spooky action on a distance“
Example: Polarisation |H> und |V> → Superposition: = 1/√2 {|H>+|V>}
2 Photons: possible polarizations: |H>1, |H>2 und |V>1, |V>2
Superposition: 2121 ||||2
1| VVHH
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
GHZ-states: SHVT = 1 SQM = Sexp = -1
QM
LR|S
|
Voltage (~Winkel)
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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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Bell statesTELEPORTATION
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Cryptography - One-Time-Pad
plain text: 4 2 3 7 1 5 0
1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 (22 Bit)binär:
1 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 (22 Bit)key:
0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 (22 Bit)Cipher:
XOR operation
plain text: (22 Bit)1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1
XOR operation
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Guessing the Secret Key
Key Size (bits)
Number Of Keys
Time at 1 µs each
Time at 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 1024bit 4096bit
Calculation time 100 000 years over 30 billion years
Quantum computer with 100MHz
Number of N 1024bit 4096bit
Calculation time 4.5 minutes 4.8 hours
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Institute of Technical Physics
Quantum cryptography or
better quantum key distribution
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Detect if someone is listening
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Example
Original: (a)
XOR XORBitwise Bitwise
Encrypted: (b)
Alice's Key Bob's Key
Decrypted: (c)
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DARPA Quantum Network
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Institute of Technical Physics
DIfm
Bomb
D
Interaction-free measurement
Elitzur, Vaidman (1993), Kwiat et al. (1995)
D
DIfm
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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 teleportation
Quantum communication
Quantum computing
Institute of Technical Physics