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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.

• EVALUATION OF THE CHARACTERISTICS OF A TWO-STAGE SYNCHRONIZATION ALGORITHM BASED ON THE SELECTION OF AN ADJACENT PAIR OF SEGMENTS WITH THE MAXIMUM TOTAL COUNT IN THE QKD SYSTEM

  К. Y. Rumyantsev, Y.К. Mironov, P.D. Mironova

  2024-08-12

  Abstract ▼

  A two-stage synchronization algorithm is proposed based on the selection of an adjacent pair of
  segments with the maximum total count in the QKD system. The algorithm is based on a well–known approach
  to reducing the time of entering into synchronism - the analysis of adjacent pairs of time segments.
  A distinctive feature of the proposed algorithm is to ensure that the probability of successful search and
  testing is not worse than the required level. It should be noted that due to the testing stage, erroneous
  decisions made at the search stage are rejected, which minimizes the probability of false synchronization
  due to the registration of noise pulses. At the search stage, the equipment sequentially registers the total
  counts from all adjacent pairs of segments. Next, a pair of segments with the maximum total count is selected,
  and the count in one of the pairs of segments reliably exceeds the values of the counts from all other
  pairs of segments, and the equipment proceeds to the testing stage. Testing consists of polling the
  photodetector during the gating pulse to re-register the count. In case of positive testing, the process of
  «rough» estimation of the moment of reception of the sync pulse is considered successfully completed,
  otherwise the equipment returns to the search in the next frame. Note that the maximum allowable number
  of frames and tests correspond to the search and testing stages, respectively. Analytical expressions are
  obtained for calculating the time and probabilistic characteristics of the search and testing stages of the
  proposed detection algorithm based on the selection of an adjacent pair of segments with the maximum
  total count, including for calculating the allowable number of frames and tests while ensuring the required probabilities of successful search and testing, respectively. It has been found that with an increase in the
  average number of photons in the sync pulse, the average number of frames and tests, as well as the average
  time of successful search and testing, decrease significantly. For example, when the average number
  of photons in a sync pulse increases by 5 times, the average number of tests for successful testing and the
  average time for successful testing decrease by 1.5 times, and the permissible number of tests by 5 times.

• PROBABILISTIC CHARACTERISTICS OF THE SYNC DETECTION ALGORITHM BASED ON THE SELECTION OF AN ADJACENT PAIR OF SEGMENTS WITH THE MAXIMUM TOTAL COUNT

  К.Е. Rumyantsev, P.D. Mironova

  2023-08-14

  Abstract ▼

  An algorithm for detecting sync signals based on the selection of an adjacent pair of segments
  with the maximum total count is proposed. This algorithm takes into account the shortcomings
  of an alternative algorithm for detecting a sync signal based on comparing the sum of samples
  from an adjacent pair of segments with a threshold level, consisting in the need to know the level of background and noise influence, which determines the threshold level and the probability
  of erroneous detection of a signal pair of segments. The dependence of the probability of an error
  in detecting a sync pulse on the average number of signal photons in a sync pulse is studied for
  various values of the number of segments in a time frame. Thus, the probability of erroneous detection
  of a sync pulse during a frame decreases significantly as the average number of photons in
  a sync pulse increases. For example, by increasing the average number of signal photons in a sync
  pulse from 1 to 5, the probability of a sync detection error is reduced by a factor of 37. It should
  be noted that the number of pairs of segments has a weak effect on the probability of erroneous
  detection, which indicates a weak effect of dark current pulses on the probabilistic characteristics
  of the proposed algorithm for detecting sync signals. Analytical expressions are obtained for accurate
  and express calculation of probabilistic characteristics of detection, taking into account the
  probability of finding a sync pulse at the boundary of two adjacent segments due to the equality of
  the duration of the sync pulse and the time segment. The results of calculation using exact expressions
  for the probability of detecting a sync pulse showed that when the signal-to-noise ratio is
  equal to 10 and higher, the influence of noise pulses on the probability of detecting a sync pulse
  can be neglected. It has been noted that the greater the number of recorded events, or, in other
  words, the greater the sum of the average numbers of signal photons and dark current pulses, the
  greater the detection probability. The calculation of the probability of detecting a sync pulse using
  simplified expressions shows a slight deviation from calculations using exact formulas, which does
  not exceed 5,3%, and the calculation using approximate expressions gives an underestimated result.
  The resulting approximate analytical expressions can be used for express calculation of the
  probability of detecting a sync pulse in a pair of segments.