institute of technical physics entanglement – beamen – quantum cryptography the weird quantum...

Institute of Technical Physics

Entanglement – Beamen – Quantum cryptography

The weird quantum world

Bernd Hüttner CPhys FInstP DLR Stuttgart


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


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


1 2

1

2

2 21 1 2 2

* *2 1 1 2

1

21

2


Double-slit experiment with Fullerenes

C 60

Diameter:C60 1 nm

dB 3 pm

Laser


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.


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 …


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


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.


Production of entangled photons

More exactly: polarizations are each other perpendicular


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!


Violation of Bell‘s inequality experimental results

GHZ-states: SHVT = 1 SQM = Sexp = -1

QM

LR|S

|

Voltage (~Winkel)


Beamen

Quantum teleportation


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.


Bell statesTELEPORTATION


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


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


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


Quantum cryptography or

better quantum key distribution


Detect if someone is listening


Example

Original: (a)

XOR XORBitwise Bitwise

Encrypted: (b)

Alice's Key Bob's Key

Decrypted: (c)


DARPA Quantum Network


DIfm

Bomb

D

Interaction-free measurement

Elitzur, Vaidman (1993), Kwiat et al. (1995)

D

DIfm


Summary and outlook

Why is this so very important?

We are in the age of quantum information processing


Gordon Moore, 1965: “Every 18 months microprocessors double in speed.”

Quantum teleportation

Quantum communication

Quantum computing

institute of technical physics entanglement – beamen – quantum cryptography the weird quantum...

Documents

classical physics

interference slide

winkel slide

perpendicular slide

quantum theory

quantum system

pm laser slide

quantum process capable