Implementation of Practically Secure Quantum Bit Commitment Protocol

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Implementation of Practically Secure Quantum Bit
Commitment Protocol

• Ariel Danan
• School of Physics Tel Aviv University
• September 2008

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• Project Members
• Ariel Danan, Yoav Linzon
• (With a lot of help from Ezra Shaked- electronic
  workshop)
• Academic supervisors
• Lev Vaidman and Shimshon Barad

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Outline

• Introduction
• Bit Commitment
• Practically Secure Quantum Bit Commitment
• Phase Encoding with Optical Fibers
• Experimental Setup
• Demonstration (Q.O. lab)
• Security Discussion
• Final Results
• Future Prospects

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Introduction

• Quantum Information ? Quantum computers
• (Grover's quantum search , Shor's quantum
  factoring .)
• Quantum Key Distribution ? No Cloning Theorem
• Unconditionally Secure Quantum Bit Commitment ?
  No Go Theorem
• Practically Secure Quantum Bit Commitment
• Based on the limitation of current technologies
• (Non-demolition measurement and long quantum
  memory)

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Introduction

• Levs Practically Secure Quantum Bit Commitment
  Protocol
• Patent Pending ? The term Non Demolition
  measurement was not used
• in the thesis
• Implementation of Practically Secure Quantum Bit
  Commitment using low cost quantum optics devices

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What is Bit Commitment?

• Committing phase
• Alice select a bit, put it in a strong box
  and sends it to Bob

0
1
or
Alice
Bob

• Opening Phase
• Alice sends the key to Bob and he reveals her
  commitment

Bob
Alice
0
1
or
Both Classical and Quantum Unconditionally
Secure bit commitment is impossible!
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Applications
?? ?? ???????!_at_

• Secure Commercial Biding
• User Authentication
• Lon distance coin Tossing
• Oblivious Transfer (Two party secure computation)

????? ??? ?? ????
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Conjugate observables

• Photon has 2 bases of polarization that dont
  commute.

Rectilinear basis eigenstates of sz
Diagonal basis eigenstates of sx
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Practical secure QBC protocol

• Committing phase
• Bob sends photons prepared randomly in one of the
  4 polarization
• to Alice.
• Bob keeps the record of when and what he sent to
  Alice.
• Alice measures all photons in one of two bases
  which manifests her commitment
  0 1.
• She announces immediately the time of detection
  of the photons.

Pulse No. 1042 (0,0)
b 0 or b 1
Pulse No. 1043 (1,1)
Pulse No. 1044 (0,1)
Pulse No. 1045 (1,1)
Pulse No. 1045
Alice
Bob
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Opening Phase-Alice reveals her commitment
(measurement base) and the measurements
outcomes.-Bob checks Alices answers.
Bob
Alice
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• Advantages
• Cheating tasks (long-time Qubit memory, Perfect
  Non-demolition Measurement) are beyond current
  technology
• No need for high fidelity (the security increase
  exponential with the number of Qubits per
  commitment).
• Short distances possibility (unlike Classical bit
  commitment)
• Since Alice dont control the information she
  gets, its more difficult for her to cheat.
• Bob cannot gain information about Alice's
  commitment or measurements outcomes before she
  announces them.

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Phase Encoding with Optical Fibers
D1 D0 Meas. Basis F2 F1 Sent Qubit
0 25 0 0,0
12.5 12.5 0 1,0
25 0 0 0,1
12.5 12.5 0 1,1
12.5 12.5 1 0,0
0 25 1 1,0
12.5 12.5 1 0,1
25 0 1 1,1
Phase Encoding Principle. Two pulses exit Bob
apparatus, and interfere on Alices side.
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Experimental Setup
2X2 fiber coupler(Beam splitter)
Nanosecond pulse laser
Phase shifter(Piezoelectric mount)
Polarization controller
Single photon detector (25 efficiency )
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Optical line performance
Visibility
L-S S-L interference pulse
S-S pulse
L-L pulse
Classical regime
Quantum regime
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Low Fidelity Source
Michelson interferometer measurement with short
pulses (a) without interference (b) (c)
interference with two different phase shifts
The system's Stability - 0.3s
Photon losses path transmissivity
Lets Go To The Q.O. LabFor a Demonstration
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Security Discussion

• Bobs Cheating
• Look for correlations between detection
  efficiency and sent qubit base.
• Alice has different setting time for different
  measurement base.
• Trojan Horse Attack

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• Alices Cheating
• Non Demolition and Quantum Memory Attack
• ('no go theorem' ) not feasible with today's
  technological limit.
• Random Base Attack
• Imposes 25 quantum bit error rate (QBER)
• Photon Number Split Attack
• To prevent this kind of attack the ratio of the
  probability
• for having two photon (or more) in a pulse and
  Alice's
• supposed detection probability must be smaller
  than one.
• Combined Attack
• Imposes

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Security Discussion with Low Fidelity source

• Bob has a low fidelity output which imposes an
  additional QBER ( )
• Random Base Attack
• Imposes
• Photon Number Split Attack
• Will not effect PNS like attack
• Combined Attack
• Imposes

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Final Results

• Opening stage results (1 photon per pulse
  )

• Each protocol took about two hours to be complete
  
• All QBC protocol results do not exceed the
  standard deviation range
• and are acceptable commitments.

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Final Results
Opening stage results(0.2 photon per pulse
)

• Each protocol took about a day to be complete.
• All QBC protocol results do not exceed the
  standard deviation range
• and are acceptable commitments.

Fragile Security- to increase security the number
of sent qubits per commitment must be
increased (2000)
Probably the first practically secure QBC system
in the world
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Future Prospects

• Improve Quantum Bit Error Rate
• Single photon source
• (Spontaneous parametric Down-Conversion)
• Improve pulse coherence

• Faster
• Real time Labview \ Design DSP circuits
• Change Piezo with Crystal for E-O modulation
  (LiNbO3)

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QA
What did he say?
You dont say!