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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.

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Security of practical quantum cryptography with heralded single photon sources

Security of practical quantum cryptography with heralded single photon sources

Mikołaj Lasota1, Rafał Demkowicz-Dobrzański2, Konrad Banaszek2

1Nicolaus Copernicus University, Torun, Poland

2University of Warsaw, Warsaw, Poland


Problems with practical realisation of quantum cryptography protocols
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)


Problems with practical realisation of quantum cryptography protocols1
Problems with practical realisation of quantum cryptography protocols

Setup imperfection:

- fibers: photon losses

- detectors: dark counts,

limited detection efficiency

- Single photon sources:

multiphoton pulses


Using heralded single photon source in quantum cryptography
Using heralded single photon source protocolsin quantum cryptography

In the case of multimode SPDC process:


Using heralded single photon source in quantum cryptography1
Using heralded single photon source in quantum cryptography protocols

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


Minimal transmission of the channel required for qkd security
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:


Key generation rate
Key generation rate security

  • 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


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
Multiplexing detector with n stages as additional detection system

1. stage

2. stage

Effective detection efficiency:




Key generation rate comparison between wcp and hsps
Key generation rate – comparison between WCP and HSPS n stages

  • 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




Conclusions
Conclusions n stages

Large transmissions

Short distances

Low transmissions

Long distances

  • 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


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