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• PROBABILISTIC CHARACTERISTICS OF THE THRESHOLD ALGORITHM FOR DETECTING SYNCHRONIZING PULSES IN THE QUANTUM KEY DISTRIBUTION SYSTEM BASED ON INFORMATION FROM AN ADJACENT PAIR OF TIME SEGMENTS

  K. E. Rumyantsev, Y. K. Mironov, P.D. Mironova

  2020-11-22

  Abstract ▼

  Quantum key distribution systems (QKD) provide increased security of transmitted information.
  For the stable operation of the QKD system, accurate synchronization of user stations is
  required with minimal time costs. An algorithm for detecting a sync signal with a threshold test is
  proposed. It is assumed that the sync pulse is simultaneously in two adjacent time segments. The
  probability of detecting a pair of time segments where a sync pulse is present is determined by the
  probability of exceeding the threshold level by the total number of signal and noise pulses recorded
  in two adjacent segments. The purpose of the research is aimed at a comparative analysis of the
  threshold level and probabilistic characteristics of synchronization equipment during threshold
  testing of each pair of time segments within a time frame, obtained when orienting on the Gauss
  and Poisson model for the number of photons and dark current pulses (DCP) received during the
  time segment analysis. The probabilistic characteristics of the detection algorithm for sync signals
  are studied in a quantum key distribution system based on a comparison of the number of photons
  from an adjacent pair of time segments with a threshold level. The application of the approximation
  of the statistical properties of the processes at the output of the photodetector by the Poisson
  law and the normal distribution is analyzed. The influence of the Poisson and Gaussian models on
  the choice of the threshold level and the calculation of the synchronization efficiency during the
  threshold testing of each pair of time segments within the time frame are estimated, obtained by
  orientation on the Gauss and Poisson models for the number of photons and DCP received during
  the analysis of the time segment. It was established that the choice of the threshold level based on
  the normal distribution gives an underestimated value. The approximation of the statistics of photons
  and pulses of dark current by a normal law provides a threshold level lower than the required
  one. Moreover, the difference grows with stricter requirements for the probability of false positives.
  The obtained probabilistic properties of the sync signal detection algorithm based on the
  analysis of the sum of counts from an adjacent pair of segments with a threshold level allow us to
  formulate recommendations for choosing an approximation of the signal statistics: for express
  calculations of probabilistic characteristics, it is advisable to use the Gaussian model; if a higher
  analysis accuracy is required, it is recommended to use the Poisson model.

• EVALUATION OF THE FUNCTIONAL ELEMENTS INFLUENCE ON THE PARAMETERS OF THE QKD SYSTEM BASED ON B92 PROTOCOL

  К.Е. Rumyantsev, P.D. Mironova, H.H. Shakir

  2022-11-01

  Abstract ▼

  The influence of the parameters of functional elements on the energy, time and probabilistic
  characteristics of the quantum key distribution system (QKD) based on the B92 protocol is studied.
  The dependences of the probability of writing correct and erroneous bits into a raw quantum
  key sequence are plotted for various lengths of a fiber-optic communication line (FOCL) and the
  use of various lasers (EML-laser; DFB-laser; VCSEL-laser and FP-laser) and photodetector
  modules (id201; id210; id220; id230). Thus, changes in the probability of writing a correct bit into
  a raw quantum key sequence are much more significant than changes in the probability of writing
  an erroneous bit (50.9 times versus 3.3 times with FWHM=80 pm and a change in the length of
  the FOCL from 10 to 100 km). This is due to the fact that with an increase in the length of the
  FOCL, the probability of the absence of registration at the receiving station of photons or dark
  current pulses (DCP) sharply increases. Numerical material indicates a direct proportional dependence
  of the probability of writing an erroneous bit on the frequency of generation of noise
  pulses of single-photon avalanche photodiodes (SAPD). So, with an increase in the frequency of
  occurrence of DCP by 60 times (from 100 to 6000 Hz), the probability of recording an erroneous
  bit also increases by 60 times (for example, with a FOCL length of 100 km – 6.39 versus 383.3).
  It has been established that the root-mean-square deviation of the photon delay time is directly proportional to the length of the FOCL and the width of the laser spectrum. With a spectrum width
  of FWHM=10 pm and an increase in the FOCL length from 10 to 100 km (by a factor of 10), the
  standard deviation of the photon delay time also increases by a factor of 10 (from 4.16 to 41.6 ps).
  To achieve the best performance of the QKD system as a whole, it is advisable to use a laser with
  a minimum width of the radiation spectrum, for example, an EML-laser. However, EML-lasers are
  considered the most complex and expensive of all the considered types of lasers, so the use of
  EML-lasers significantly increases the cost of the entire QKD system.