Multipartite entanglement, quantum communication and computation

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Multipartite entanglement, quantum communication
and computation

• Dmitri Horoshko and Sergei Kilin
• Institute of Physics of the National Academy of
  Sciences of Belarus, Minsk

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I The notion of entanglementII Applications of
entanglement quantum computation and quantum
cryptography
Plan of report
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Part IThe notion of entanglement
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Einstein-Podolsky-Rosen paradox (1935)
A
B
After measuring one particle, another particle
changes its state discontinuously
Measuring the momentum of A
Measuring the position of A
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Entanglement pure states
Definition a state of two systems A and B is
entangled if it does not factor
(E.Schrödinger, Naturwissenschaften 1935)
Measure of entanglement von Neumann entropy of
one system
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Entanglement mixed states
Definition a state of two systems A and B is
entangled if it is inseparable
Criterion (sufficient) violation of positivity
of partial transpose
Criterion is necessary and sufficient for
or systems In the general case no
necessary and sufficient criterion and no measure
are known
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Entanglement in optics
Discrete observable polarization of single
photon Horizontal or Vertical
Single photon is a two-level quantum system, like
a spin-½ particle Such a system is called quantum
bit or qubit
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Entanglement in optics
Kwiat et al., PRL 75 4337 (1995)
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Quantum teleportation
Classical channel
Alice
Bob


Y
gt
(agt3 b b gt3)/?2

f

f
3
1
2
1

Y
gt
3
2
-
Y
gt
1


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?-gt12( a gt 3 b b gt 3)/?2 ?gt12(-a gt
3 b b gt 3)/?2 Fgt12(-b gt 3 a b gt
3)/?2 F-gt12( b gt 3 a b gt 3)/?2
-
Y
gt


-


(
)
/
2
b
b
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2
3
2
3
A.Zeilinger et al., Nature 1997
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Fidelity
We expect
We get How far is from ?

Measure of distance - fidelity
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Multipartite entanglement
Example Greenberger-Horne-Zeilinger state of
three systems
In the general case no criterion is
known Entanglement witness - operator
A for any separable state for some
inseparable state
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Part IIApplications of entanglementquantum
computation and quantum cryptography
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Cryptography

• ELSIE PREPARE TO MEET THY GOD

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Cryptography

• Symmetric cryptosystems (with a secret key)
• Public-key cryptosystems (asymmetric)
• Hybrid cryptosystems

• Require a secret key distributed between all
  participants
• Perfect security (Shannon 1949) . Prob(break)
  Prob(guess)

• Do not require a key distribution step
• Based on one-way functions
• Provide conditional security

• Key is distributed by a public-key cryptosystem
• Message is transmitted by a symmetric
  cryptosystem
• Provide conditional security

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Non-polynomial algorithms
Number of algorithm steps gt poly (log y), for y ?
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One-way function
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Quantum algorithm for factorization
In 1994 ?. Peter Shor (USA) published a
polynomial algorithm of factorization on a
quantum computer
y p1p2pk
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Quantum computer
x 1 0 1 1 0 0
Register 1
Register 2
f(x) 0 1 1 0 1 1
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Quantum computer
Register 1
Register 2
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Quantum computers D-Wave
Orion
Quantum chip based on superconducting circuits
Last achievement 28 qubits. Not universal
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Quantum computers in Belarus

• 6th Framework project EQUIND
• creation of universal quantum processor on
  the basis of diamond

Nitrogen N
Vacancy V
Qubits nuclear spins of the isotopic carbon 13?
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Quantum cryptography

• Principle encoding information in polarization
  of a single photon
• Eavesdropping is impossible because of
  impossibility of cloning an unknown quantum state

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Quantum cryptography

• id Quantique (Geneva)
• MagiQ (New-York)
• Properties
• Photons in fibre
• Protocol BB84
• Phase coding
• Distance up to 70 km
• Rate 1000 bit/s
• USB interface
• Classical channel via Ethernet
• Cost 100 000 EUR

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Quantum cryptography in Minsk
1. Signal generator 2. VCSEL 3. Temperature
controller 4. Fiber-optic variable attenuator 5.
Fixed Delay 6. Nonpolarizing beamsplitter 2?2
7. Fused 2?2 fiber-optic coupler 8. Polarization
controller 9. Delay line 10. Thermobox with
active stabilization 11. Single-photon detector
module 12. Time-interval counter