Implementation of Practically Secure Implementation of Practically Secure Quantum Bit Commitment ProtocolQuantum Bit Commitment Protocol
Ariel Danan Ariel Danan
School of Physics Tel Aviv UniversitySchool of Physics Tel Aviv University
September 2008September 2008
Project Members:Project Members: Ariel Danan, Yoav LinzonAriel Danan, Yoav Linzon(With a lot of help from Ezra Shaked- electronic workshop)(With a lot of help from Ezra Shaked- electronic workshop)
Academic supervisors:Academic supervisors: Lev Vaidman and Shimshon BaradLev Vaidman and Shimshon Barad
OutlineOutline Introduction Introduction Bit CommitmentBit Commitment Practically Secure Quantum Bit CommitmentPractically Secure Quantum Bit Commitment Phase Encoding with Optical FibersPhase Encoding with Optical Fibers Experimental SetupExperimental Setup Demonstration (Q.O. lab)Demonstration (Q.O. lab) Security Discussion Security Discussion Final ResultsFinal Results Future ProspectsFuture Prospects
IntroductionIntroduction Quantum Information Quantum Information →→ Quantum computers Quantum computers
((Grover's quantum searchGrover's quantum search , , Shor's quantum factoringShor's quantum factoring ….)….) Quantum Key Distribution Quantum Key Distribution ↔↔ ‘No Cloning Theorem’ ‘No Cloning Theorem’
Unconditionally Secure Quantum Bit Commitment Unconditionally Secure Quantum Bit Commitment →→ ‘No Go Theorem’ ‘No Go Theorem’ Practically Secure Quantum Bit CommitmentPractically Secure Quantum Bit Commitment
Based on the limitation of current technologiesBased on the limitation of current technologies(Non-demolition measurement and long quantum memory)(Non-demolition measurement and long quantum memory)
IntroductionIntroduction
Lev’s Practically Secure Quantum Bit Commitment ProtocolLev’s Practically Secure Quantum Bit Commitment ProtocolPatent Pending Patent Pending →→ The term Non Demolition measurement was not used The term Non Demolition measurement was not used
in the thesis in the thesis
Implementation of Practically Secure Quantum Bit Commitment using low Implementation of Practically Secure Quantum Bit Commitment using low cost quantum optics devicescost quantum optics devices
What is Bit Commitment?What is Bit Commitment? Committing phase:Committing phase: Alice select a bit, put it in a strong box and sends it to Bob Alice select a bit, put it in a strong box and sends it to Bob
0 1or
Bob
Alice
Opening Phase:Opening Phase: Alice sends the key to Bob and he reveals her commitmentAlice sends the key to Bob and he reveals her commitment
Alice
10 or
Bob
Both Classical and Quantum Unconditionally Secure bit Both Classical and Quantum Unconditionally Secure bit commitment is impossible!commitment is impossible!
ApplicationsApplications Secure Commercial BidingSecure Commercial Biding
User AuthenticationUser Authentication
Lon distance coin TossingLon distance coin Tossing
Oblivious Transfer Oblivious Transfer (Two party secure computation)(Two party secure computation)
רק לא גיידאמק!
#@
?אתמול היה
לי יותר
Conjugate observablesConjugate observables
Photon has 2 bases of polarization that don’t commute. Photon has 2 bases of polarization that don’t commute.
Rectilinear basis:eigenstates of σz
Diagonal basis:eigenstates of σx
Practical secure QBC protocolPractical secure QBC protocolCommitting phase:Committing phase: Bob sends photons prepared randomly in one of the 4 polarization Bob sends photons prepared randomly in one of the 4 polarization
{ } to Alice.{ } to Alice. Bob keeps the record of when and what he sent 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 Alice measures all photons in one of two bases which manifests her
commitment { } = commitment { } = 00 { } = { } = 11.. She announces immediately the time of detection of the photons.She announces immediately the time of detection of the photons.
BobAlice
b =0or
b =1
Pulse No. 1045 Pulse No. 1045 (1,1)
Pulse No. 1044 (0,1)
Pulse No. 1043 (1,1)
Pulse No. 1042 (0,0)
OpeningOpening PhasePhase::-Alice reveals her commitment (measurement base) and the measurements Alice reveals her commitment (measurement base) and the measurements outcomes.outcomes.
--Bob checks Alice’s answers.Bob checks Alice’s answers.
BobAlice
AdvantagesAdvantages
1.1. Cheating tasks (long-time Qubit memory, Perfect Non-Cheating tasks (long-time Qubit memory, Perfect Non-demolition Measurement) are beyond current technologydemolition Measurement) are beyond current technology
2.2. No need for high fidelity (the security increase exponential No need for high fidelity (the security increase exponential with the number of Qubits per commitment).with the number of Qubits per commitment).
3.3. Short distances possibility (unlike Classical bit Short distances possibility (unlike Classical bit commitment)commitment)
4.4. Since Alice don’t control the information she gets, it’s more Since Alice don’t control the information she gets, it’s more difficult for her to cheat.difficult for her to cheat.
5.5. BobBob cannot gain information about cannot gain information about AliceAlice's commitment or 's commitment or measurements outcomes before she announces them. measurements outcomes before she announces them.
Phase Encoding with Optical FibersPhase Encoding with Optical Fibers
SentQubitΦ1Φ2
Meas.BasisD0D1
0,0025%0%
1,0012.5%12.5%
0,100%25%
1,1012.5%12.5%
0,0112.5%12.5%
1,0125%0%
0,1112.5%12.5%
1,110%25%1{ } 1{ 0}
1
3{ }
2
1{ }
2
Phase Encoding Principle. Two pulses exit Bob apparatus, and interfere on Alice’s side.
2
2
2
0
2
0
0
0
0
0
2
2
3
2
3
2
Experimental SetupExperimental Setup
Transmitter
Pulse modulator
EncoderLaser ND
filter
Optical fiber
1
Receiver
2(SPD(1
SPD(0(
Encoder
Trigger Card
Synchronizer
DataAcquisition
Bob
Alice
.Serial com
.P.C
.P.C
-0.250.000.25
-0.250.00
0.25
-0.25 0.000.25
-0.25 0.000.25
-0.2
50.
000.
25-0
.25
0.00
0.25
-0.25 0.00 0.25 -0.25 0.00 0.25 -0.25 0.00 0.25 -0.25 0.00 0.25
Single photon Single photon detector (~25% detector (~25%
efficiency )efficiency )
2X2 fiber coupler2X2 fiber coupler(Beam splitter)(Beam splitter)
Polarization Polarization controllercontroller
Phase shifterPhase shifter(Piezoelectric (Piezoelectric
mount)mount)
Nanosecond Nanosecond pulse laserpulse laser
Optical line performance Optical line performance
minmax
minmax
II
IIV
Visibility
S-S pulse
L-S + S-L interference pulse
L-L pulse
Classical regime
Quantum regime
Low Fidelity SourceLow Fidelity Source
Michelson interferometer measurement with short pulses: (a) without interference; (b) & (c) interference with two different phase shifts
Let’s Go To The Q.O. LabLet’s Go To The Q.O. LabFor a DemonstrationFor a Demonstration
The system's Stability - The system's Stability - ~0.3s ~0.3s
Photon lossesPhoton losses – path transmissivity – path transmissivity
Security DiscussionSecurity Discussion
BobBob’s Cheating:’s Cheating:
1.1. Look for correlations between detection efficiency and Look for correlations between detection efficiency and sent qubit base.sent qubit base.
2.2. Alice has different setting time for different measurement Alice has different setting time for different measurement base.base.
3.3. Trojan Horse Attack Trojan Horse Attack
AliceAlice’s Cheating:’s Cheating:
1.1. Non Demolition and Quantum Memory AttackNon Demolition and Quantum Memory Attack('no go theorem' ); not feasible with today's technological limit.('no go theorem' ); not feasible with today's technological limit.
2.2. Random Base AttackRandom Base AttackImposes 25% quantum bit error rate (QBER)Imposes 25% quantum bit error rate (QBER)
3.3. Photon Number Split AttackPhoton Number Split AttackTo prevent this kind of attack the ratio of the probability To prevent this kind of attack the ratio of the probability
for having two photon (or more) in a pulse and Alice'sfor having two photon (or more) in a pulse and Alice's
supposed detection probability must be smaller than one.supposed detection probability must be smaller than one.
4.4. Combined AttackCombined AttackImposes Imposes
( )
1100%
4QBER
Security Discussion with Low Security Discussion with Low Fidelity sourceFidelity source
BobBob has a low fidelity output which imposes an additional has a low fidelity output which imposes an additional QBER (QBER ( ) )
1.1. Random Base Attack:Random Base Attack:ImposesImposes
3.3. Photon Number Split Attack:Photon Number Split Attack:Will not effect PNS like attack Will not effect PNS like attack
4.4. Combined Attack:Combined Attack:Imposes Imposes
B
50%
2BQBER
1 1100%
4 2 BQBER
Final ResultsFinal Results
Opening stage results (1 photon per pulse 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.
1
Final ResultsFinal Results
•Each protocol took about a day to be complete.
•All QBC protocol results do not exceed the standard deviation range
and are acceptable commitments.
Probably the first practically Probably the first practically secure QBC system in the secure QBC system in the
worldworld
Opening stage results(0.2 photon per Opening stage results(0.2 photon per pulse ) pulse )
Fragile Security- to increase security the number of sent qubits perFragile Security- to increase security the number of sent qubits per
commitment must be increased (2000)commitment must be increased (2000)
1
Future ProspectsFuture Prospects
Improve Quantum Bit Error RateImprove Quantum Bit Error Rate1.1. Single photon source Single photon source
(Spontaneous parametric Down-Conversion)(Spontaneous parametric Down-Conversion)
2.2. Improve pulse coherence Improve pulse coherence
FasterFaster1.1. Real time Labview \ Design DSP circuitsReal time Labview \ Design DSP circuits2.2. Change Piezo with Crystal for E-O modulation (LiNbO3) Change Piezo with Crystal for E-O modulation (LiNbO3)
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