Quantum Cryptography

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Quantum Cryptography

• December, 3rd 2007
• Philippe LABOUCHERE
• Annika BEHRENS

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1. Introduction
2. Photon sources
3. Quantum Secret Sharing

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• Introduction
• Photon sources
• Quantum Secret Sharing

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How to measure information (1)

• Claude E. Shannon 1948
• Information entropy
• Mutual information

bits
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How to measure information (2)

• Relation between H and I
• Mutual information between 2 parties

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Venn diagrams
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The BB84 protocol
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The BB84 protocol principle

• 2 conjugate basis
• Information encoded in photons polarization
• ? 0 /
• ? 1 \
• Quantum classical channels used for key exchange

Charles H. Bennett
Gilles Brassard
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From random bits to a sifted key
Alices random bits 0 1 1 O O 1
Random sending bases D D R R D R
Photon Alice sends / \ /
Random receiving bases R D R D D R
Bits as received by Bob 1 1 1 0 0 1
Bob reports basis of received bits R D R D D R
Alice says which were correct no OK OK no OK OK
Presumably shared information . 1 1 . 0 1
Bob reveals some key bits at random . . 1 . 0 .
Alice confirms them . . OK . OK .
Remaining shared bits . 1 . . . 1
Quantum transmission
Public discussion
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Mutual information vs quantum bit error rate
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The no-cloning theorem

• Dieks, Wootters, Žurek 1982
• It is forbidden to create
• identical copies of an arbitrary unknown quantum
  state.
• Quantum operations unitary linear
  transformations on the state of a quantum system

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• Introduction
• Photon sources
• Quantum Secret Sharing

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Sources of photons

• Thermal light
• Coherent light
• Squeezed light

Average photon number of photons in a mode Number
of photons
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Faint-laser pulses

• ltngt µ 0.1 photon / pulse
• Photon-number splitting attack!
• Dark counts of detectors vs high pulse rate
  weaker pulses

Detection yield Transmission efficiency
!
Tradeoff
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Entangled photon pairs

• Spontaneous
• Parametric
• Down
• Conversion
• Idler photon acts as trigger for signal photon
• Very inefficient

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Single-photon sources

• Intercept/resend attack
• gt error rate lt dark count rate !
• Condition for security
• Drawback dark counts afterpulses

Detection yield
Transmission efficiency
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Practical limits of QC

• Realization of signal
• Stability under the influence of the environment
  (transportation)
• - Birefringence
• - Polarization dispersion
• - Scattering
• Need of efficient sources detectors
  (measurements)

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Bite rate as function of distance after error
correction and privacy amplification
Pulse rate 10 MHz µ 0.1 (faint laser pulses)
Losses _at_ 800nm 2dB / km _at_ 1300 nm 0.35dB
/ km _at_ 1550 nm 0.25 dB /km
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1. Introduction
2. Photon sources
3. Quantum Secret Sharing

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Quantum Secret Sharing (1)
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QSS (2)

• N-qubit GHZ source
• Define

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Goodbye GHZ, welcome single qubit
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Sequentially polarized single photon protocol

Original BB84 Modified BB84
Diagonal and Rectilinear bases Classes X and Y
/ and 0 and \ 1 fj 0, p/2 0 fj p, 3p/2 1
Correlated results if same bases used Correlated results if
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Questions ?