Вестник Тамбовского государственного технического университета
The Effect of Single Photon Transmission Time on the Probability of Erroneous Registration of Asynchronous Data of Quantum Cryptographic Communication Channels
Expressions are determined to estimate the probabilities of erroneous recording of binary data of a quantum-cryptographic communication channel containing a photon counter with an extending dead time.According to the results of mathematical modeling, the dependences of the probabilities of erroneous data recording at the output of the communication channel are established on the average single-photon transmission time of the characters "0" and "1", on the basis of which the choice of the smallest average transmission time per bit (character), providing the smallest loss of information transmitted, is justified.
Expressions are determined to estimate the probabilities of erroneous recording of binary data of a quantum-cryptographic communication channel containing a photon counter with an extending dead time.According to the results of mathematical modeling, the dependences of the probabilities of erroneous data recording at the output of the communication channel are established on the average single-photon transmission time of the characters "0" and "1", on the basis of which the choice of the smallest average transmission time per bit (character), providing the smallest loss of information transmitted, is justified.
An asynchronous quantum-cryptographic communication channel with a receiving module based on a photon counter with a dead time of an extending type was investigated. An expression for estimating the ratio of the probability of erasing binary symbols "0" P(–/0) to the probability of these symbols being erroneous Perr0 has been obtained. Based on the results of mathematical modeling, the dependences of the ratio P(–/0) / Perr0 on the average count rate of signal pulses at the output of the photon counter during the transmission of symbols “0” ns0 for various average duration of dead time of the extended type τd were established. The performed studies have shown that with an increase in ns0, these dependences at first practically do not change and have values close to unity, but then they drop down to the lowest values and go into saturation. This takes place both in the absence of a dead time of the prolonging type, and in its presence.
Expression for estimating the reliability of information during its transmission through quantum-cryptographic communication channel that contains a dead time photon counter has been obtained in this research. According to the results of mathematical modeling, the dependence of the reliability of the received data on the average time of single photon transmission of information was established. Studies have shown that with an increase in the average time of single photon transmission of information, these dependences grow, reaching saturation. Moreover, with equal parameters with an increase in the average duration of the dead time of a prolonging type, saturation occurs at large values of the average time of a single photon transmission of information.
When measuring low-power optical signals, it is necessary to ensure the highest reliability of the received data, which is especially important for single-photon communication channels. This determines the expediency of using photon counters as receiving modules for such channels. They are highly sensitive, but are characterized by data recording errors. Therefore, the purpose of this work was to investigate the influence of the intensity of the registered optical radiation J0 during the transmission of binary symbols “0” on the probability of registering symbols “1” at the output of the communication channel in the presence of symbols “0” at its input P(1/0). The statistical distributions of the mixture of the number of dark and signal pulses at the output of the photon counter during the registration of binary symbols “0” Pst0 (N ) were determined. To do this, a technique was used to reduce information loss. As a result, the minimum probability P(1/0) was reached. The probabilities P(1/0) were calculated for a communication channel containing a photon counter as a receiving module. This calculation was carried out at different values of the supply voltage of the avalanche photodetector U and the intensity of the optical signal used to transmit the binary symbols “0” J0 . The experimental results showed that with increasing optical signal intensity J0 , the dependences P(1/0) on J0 initially remain almost unchanged and retain a constant value. However, with a further increase in J0 , there is a linearly increasing character of the dependences P(1/0) on J0 . Moreover, with other equal reception parameters, such a character of the dependences P(1/0) on J0 begins to manifest itself at higher intensities of the optical signal J0 with an increase in the supply voltage of the avalanche photodetector.
Receiving modules of single-photon communication systems should provide the smallest loss of transmitted information when measuring low-power optical signals. In this regard, it is advisable to use photon counters. They are the most highly sensitive, but characterized by data recording errors. The aim of this work was to develop a method for determining the intensity of recorded optical signal in a singlephoton communication channel with a receiving module based on a photon counter, which ensures the least probability of erroneous registration of transmitted binary symbols. Methods of achieving the least loss of information in asynchronous photon binary communication channel with a receiver-based photon counter has been developed. A device for implementing this methods has been created. The method is based on using the statistical distribution of the mixture of the number of dark and signal pulses received at the output of the photon counter when registering binary symbols "0" P st 0 ( N ) and symbols "1" P st 1 ( N ). The essence of the method consists in determining the intensities of optical signals for transmitting binary symbols ("0" and "1") and threshold levels of the pulses N 1 and N 2 registered at the output of the photon counter. The method allows to determine the lower and upper threshold levels of recorded pulses and the intensity of optical signals in the transmission of binary data. Moreover, the probability of erroneous registration of binary symbols is minimal.
When measuring low-power optical signals in single-photon communication channels, the receiving modules must ensure the minimum probability of erroneous data recording. In this regard, it is advisable to use photon counters. They are highly sensitive, but are characterized by data recording errors. The aim of the work was to determine the effect of intensity of optical signal on the probability of erroneous data recording in a single-photon communication channel with a receiving module based on a photon counter. Based on the results of experimental studies, the dependences of the probability of erroneous registration of binary symbols «0» Perr 0 on the intensity of the optical signal J0 , used to transmit these symbols for various supply voltages of the avalanche photodetector U, were obtained. It was found that with an increase of intensity of the optical signal, the dependences Perr 0(J0) first decrease, reaching their lowest value, and then increase. The performed assessment showed that the lowest probability of erroneous registration the binary symbols «0» for the investigated communication channel is equal to 17,56 • 10-2 and corresponds to J0 = 52,41 • 10-2 rel. units and U = 52,54 V.
Receiving modules of single-photon communication channels should provide the least loss of transmitted information when measuring low-power optical signals. In this regard, it is advisable to use photon counters. They are highly sensitive, but are characterized by data logging errors. Therefore, the purpose of this work was to investigate the effect of the intensity of the recorded optical radiation during the transmission of binary symbols «0» on the probability of erasing these symbols in a single-photon communication channel containing a photon counter based on an avalanche photodetector as a receiving module with a passive avalanche suppression scheme. The lower and upper threshold levels of pulses recorded at the output of the photon counter, as well as the statistical distributions of the mixture of the number of dark and signal pulses at the output of the photon counter when registering binary symbols «0» Pst0( N ) and «1» Pst1( N ) were determined. For this, a technique was used to reduce information loss. As a result, the minimum probability of erasing binary symbols «0» P(–/0) was achieved. The performed experimental results showed that to achieve the minimum probability of erasing binary symbols «0» P(–/0) = 0,11·10−2, it is important to select not only the intensity of the used optical radiation J , but also the supply voltage of the avalanche photodetector U, at which the dead time of the photon counter is −2 minimal, and its quantum detection efficiency is maximum: J0 ≥ 98,94·10−2 rel. units and U = 52,54 V.