1. 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

2. 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)

3. Problems with practical realisation of quantum cryptography protocols Setup imperfection: - fibers: photon losses - detectors: dark counts, limited detection efficiency - Single photon sources: multiphoton pulses

4. Using heralded single photon source in quantum cryptography In the case of multimode SPDC process:

5. 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

6. 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:

7. 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

8. 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 )

9. Multiplexing detector with n stages as additional detection system 1. stage2. stage Effective detection efficiency:

10. Key generation rate for a multiplexing detection system with n stages

12. 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

13. Key generation rate for WCP and HSPS cryptography

15. 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 Large transmissions Short distances Low transmissions Long distances