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Security of practical quantum cryptography with heralded single photon sources. Mikołaj Lasota 1 , Rafał Demkowicz-Dobrzański 2 , Konrad Banaszek 2 1 Nicolaus Copernicus University, Torun, Poland 2 University of Warsaw, Warsaw, Poland. - PowerPoint PPT Presentation
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Security of practical quantum cryptography with heralded single
photon sources
Mikołaj Lasota1, Rafał Demkowicz-Dobrzański2, Konrad Banaszek2
1Nicolaus Copernicus University, Torun, Poland2University of Warsaw, Warsaw, Poland
Problems with practical realisation of quantum cryptography protocols
Setup imperfection:- fibers: photon losses
- detectors: dark counts, limited detection efficiency
- Single photon sources: multiphoton pulses
• G. Brassard, N. Lutkenhaus, T. Mor, B. Sanders; Phys. Rev. Lett. 85, 1330 (2000)
5.1n
n
np
Problems with practical realisation of quantum cryptography protocols
Setup imperfection:
- fibers: photon losses
- detectors: dark counts,
limited detection efficiency
- Single photon sources:
multiphoton pulses
np3.0n
n
np
n
3.0n
Using heralded single photon source in quantum cryptography
222
11004
2
In the case of multimode SPDC process:
Using heralded single photon source in quantum cryptography
• Definition: - probability of exactly one click in the heralding detection system, while there were „i” pairs of photons generated by Alice’s source
• Ideally: - -
• In reality we have due to: - dark counts- limited detection efficiency- losses- partial photon number resolution
iq
020 qq11 q
0,1,0 210 qqq
Minimal transmission of the channel, required for QKD security
• Explicit formula for depends on:- the protocol used by Alice and Bob- the list of assumptions about Eve’s possibilities of attack
• Ideal single photon source:~ probability of a dark count in Bob’s detector
• Attenuated laser as a source of single photons:~ (probability of a dark count in Bob’s detector)1/2
• Heralded single photon source:
21
20minminmin q
qqTTT WCPSGLHSPS
minT
SGLTmin
WCPTmin
Key generation rate• Definition: the amount of bits of secure key produced by a given
setup per unit of time
• Motivation: not only the maximal distance, but also the speed of QKD is important
• General formula for key generation rate:
- - repetition rate of Alice’s source
- - probability of a click in Bob’s detector when Alice’s source emits a pulse
- - probability of accepting the bit by Alice and Bob during the stage of sifting (basis reconciliation)
- - mutual information between X and Y
AEABsift IIppRk exp
expp
siftp
R
XYI
Key generation rate – dependence on complete transmission of the channel
(Alice’s detector: efficiency - 60%, dark counts probability – 10-6, Bob’s detector: dark counts probability – 10-5)
Multiplexing detector with n stages as additional detection system
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1. stage 2. stage
nCAA ~
Effective detection efficiency:
Key generation rate for a multiplexing detection system with n stages
Key generation rate for a multiplexing detection system with n stages
Key generation rate – comparison between WCP and HSPS
• Approximately, in the absence of dark counts:
• For the multiplexing detection system considered here:
• Conclusion: for we can increase key generation rate for large values of using HSPS source with multiplexing detection system only if we have
WCPHSPS Kq
qK
2
21
An
AdAq
q
~
2
122
~
02
21
3
2~ A
nT
Key generation rate for WCP and HSPS cryptography
Key generation rate for WCP and HSPS cryptography
Conclusions
• For short distances HSPS cryptography with multiplexing can beat WCP only if we have binary detectors with very good detection efficiency
• For intermediate distances HSPS cryptography with multiplexing is better than HSPS with single binary detector
• For long distances (close to the maximal distance of security) HSPS cryptography with single binary detector is the best
WCPHSPS Kq
qK
2
21
21
20minminmin q
qqTTT WCPSGLHSPS
Large transmissions
Short distances
Low transmissions
Long distances
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