Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

The energetical threshold of optical information detection due to thermal noise

Andris O. Ozols, Jurģis Poriņš, Girts Ivanovs

Published Sep 10, 2008• 0 citations
Publisher

Abstract

The minimum average optical signal power, Pmin., in optical communications is limited by the photodetector quantum efficiency and by noise. In this paper, the effect of thermal photons irradiated by all materials at absolute temperatures T>0 on optical information detection in communication lines is quantitatively considered. Usually, only the thermal current fluctuations in the photodetector are taken into account. Basing on the negentropy principle of information, assuming the Planck's blackbody radiation spectral distribution of photons, and describing the optical communication channel as non-symmetric noisy binary channel we have calculated the minimum energy required for the detection of one bit of information, ε= 6.5kT/bit, k =1.38×10-23 J/K being the Boltzmann constant. This ε value corresponds to the large error probability q = 0.20. At T = 20°C ε=4.05×10-21 J/bit and for the bit rate of R = 1010 bits/s one finds Pmin = Rε2.63×10-7 mW. In the case of more realistic value of q=10-9 ε=26kT/bit=1.05×10-19 J/bit, Pmin = 1.05×10-6 mW. This is only about 10 times lower than the quantum photodetection limit of conventional photodetectors. For more sensitive photodetectors the thermal photon noise can become important. It is shown that the minimum signal energy estimate ε≈10-19 J/bit is applicable also in a wider error probability range of q=10-3-10-15.

DOI
10.1117/12.815191

Related papers

Minimum energy per bit in high bit rate optical communications and quantum communications

Philippe B. Gallion, Francisco Javier Mendieta

Optical direct detection usually operates far above the quantum limit, due to the high thermal noise level of PIN photodiodes. For signal energy at the quantum level, the thermal effects in photon counters are also a strong limitation. The optical amplification or the heterodyne detection of the 2 quadratures of the field, widely used in high bit rate and long haul optical systems, overcome this limitation at the expense of a minimum 3db noise figure. By allowing a noise free mixing gain, as well as single quadrature measurements, the balanced homodyne receiver is allowed to reach quantum noise limited operation. The aim of this paper is to review the different quantum receiver implementations and to compare the minimum signal energy required to achieve a given bit error rate, or a given bit erasure rate, in high bit rate communications and quantum communications. Application to quantum cryptography will be also addressed.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 13, 2011•1 citation

Binary optical communication in single-mode and entangled quantum noisy channels

Stefano Olivares, Matteo G. A. Paris

We address binary optical communication in single-mode and entangled quantum noisy channels. For single mode we present a systematic comparison between direct photodetection and homodyne detection in realistic conditions, i.e. taking into account the noise that occurs during both the propagation and the detection of the signals. We then consider entangled channels based on a twin-beam state of radiation, and show that with realistic heterodyne detection the error probability at fixed channel energy is reduced in comparison with the single-mode cases for a large range of values of quantum efficiency and noise parameters.

arXiv:quant-ph/0309096•Journal of Optics B Quantum and Semiclassical Optics•Nov 5, 2003•31 citations

Quantum noise limited optical communication with low probability of detection

Boulat A. Bash, Saikat Guha, Dennis Goeckel +1 more

We demonstrate the achievability of a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over the single-mode lossy bosonic channel if either the eavesdropper's measurements or the channel itself is subject to the slightest amount of excess noise. Specifically, Alice can transmit O(√n) bits to Bob over n channel uses such that Bob's average codeword error probability is upper-bounded by an arbitrarily small δ > 0 while a passive eavesdropper, Warden Willie, who is assumed to be able to collect all the transmitted photons that do not reach Bob, has an average probability of detection error that is lower-bounded by 1/2 - ε for an arbitrarily small ε > 0. We analyze the thermal noise and pure loss channels. The square root law holds for the thermal noise channel even if Willie employs a quantum-optimal measurement, while Bob is equipped with a standard coherent detection receiver. We also show that LPD communication is not possible with coherent state transmission on the pure loss channel. However, this result assumes Willie to possess an ideal receiver that is not subject to excess noise. If Willie is restricted to a practical receiver with a non-zero dark current, the square root law is achievable on the pure loss channel.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2013•22 citations

Measurement of the Probability of a Binary Symbol «0» Erasing in a Single-Photon Asynchronous Communication Channel with a Receiver Based on a Photon Counter

A. M. Timofeev

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.

Devices and Methods of Measurements•Jun 25, 2021•1 citation

Probability of Erroneous Data Registration in a Single Photon Erasure-Type Communication Channel with a Receiver Based on a Photon Counter

A. M. Timofeev

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.

Devices and Methods of Measurements•Jul 6, 2022•0 citations

Quantum theory of the homodyne-direct receiver

Masashi Ban

A quantum-communication-theoretical approach to the homodyne-direct receiver is presented and used to obtain the quantum detection operators and average probability of error for any binary quantum-state signal. The effect of the quantum efficiency η of a photodetector used in the receiver is taken into account. Which quantum states have been received is determined by comparing the read-out of the receiver with a certain decision level; so the dependences of the detection operators and average probability of error on a decision level are also considered. As a quantum-state signal, the binary phaseshift keyed signal including thermal noise is investigated in detail, and the condition necessary for the average probability of error of the homodyne-direct receiver to be smaller than the standard quantum limit (the short noise limit) of the signal detection is obtained.

Journal of Modern Optics•Jun 1, 1997•7 citations
The minimum average optical signal power, Pmin., in optical communications is limited by the photodetector quantum efficiency and by noise. In this paper, the effect of thermal photons irradiated by all materials at absolute temperatures T>0 on optical information detection in communication lines is quantitatively considered. Usually, only the thermal current fluctuations in the photodetector are taken into account. Basing on the negentropy principle of information, assuming the Planck's blackbody radiation spectral distribution of photons, and describing the optical communication channel as non-symmetric noisy binary channel we have calculated the minimum energy required for the detection of one bit of information, ε= 6.5kT/bit, k =1.38×10-23 J/K being the Boltzmann constant. This ε value corresponds to the large error probability q = 0.20. At T = 20°C ε=4.05×10-21 J/bit and for the bit rate of R = 1010 bits/s one finds Pmin = Rε2.63×10-7 mW. In the case of more realistic value of q=10-9 ε=26kT/bit=1.05×10-19 J/bit, Pmin = 1.05×10-6 mW. This is only about 10 times lower than the quantum photodetection limit of conventional photodetectors. For more sensitive photodetectors the thermal photon noise can become important. It is shown that the minimum signal energy estimate ε≈10-19 J/bit is applicable also in a wider error probability range of q=10-3-10-15.
Optical direct detection usually operates far above the quantum limit, due to the high thermal noise level of PIN photodiodes. For signal energy at the quantum level, the thermal effects in photon counters are also a strong limitation. The optical amplification or the heterodyne detection of the 2 quadratures of the field, widely used in high bit rate and long haul optical systems, overcome this limitation at the expense of a minimum 3db noise figure. By allowing a noise free mixing gain, as well as single quadrature measurements, the balanced homodyne receiver is allowed to reach quantum noise limited operation. The aim of this paper is to review the different quantum receiver implementations and to compare the minimum signal energy required to achieve a given bit error rate, or a given bit erasure rate, in high bit rate communications and quantum communications. Application to quantum cryptography will be also addressed.
We address binary optical communication in single-mode and entangled quantum noisy channels. For single mode we present a systematic comparison between direct photodetection and homodyne detection in realistic conditions, i.e. taking into account the noise that occurs during both the propagation and the detection of the signals. We then consider entangled channels based on a twin-beam state of radiation, and show that with realistic heterodyne detection the error probability at fixed channel energy is reduced in comparison with the single-mode cases for a large range of values of quantum efficiency and noise parameters.
We demonstrate the achievability of a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over the single-mode lossy bosonic channel if either the eavesdropper's measurements or the channel itself is subject to the slightest amount of excess noise. Specifically, Alice can transmit O(√n) bits to Bob over n channel uses such that Bob's average codeword error probability is upper-bounded by an arbitrarily small δ > 0 while a passive eavesdropper, Warden Willie, who is assumed to be able to collect all the transmitted photons that do not reach Bob, has an average probability of detection error that is lower-bounded by 1/2 - ε for an arbitrarily small ε > 0. We analyze the thermal noise and pure loss channels. The square root law holds for the thermal noise channel even if Willie employs a quantum-optimal measurement, while Bob is equipped with a standard coherent detection receiver. We also show that LPD communication is not possible with coherent state transmission on the pure loss channel. However, this result assumes Willie to possess an ideal receiver that is not subject to excess noise. If Willie is restricted to a practical receiver with a non-zero dark current, the square root law is achievable on the pure loss channel.
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.
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.
A quantum-communication-theoretical approach to the homodyne-direct receiver is presented and used to obtain the quantum detection operators and average probability of error for any binary quantum-state signal. The effect of the quantum efficiency η of a photodetector used in the receiver is taken into account. Which quantum states have been received is determined by comparing the read-out of the receiver with a certain decision level; so the dependences of the detection operators and average probability of error on a decision level are also considered. As a quantum-state signal, the binary phaseshift keyed signal including thermal noise is investigated in detail, and the condition necessary for the average probability of error of the homodyne-direct receiver to be smaller than the standard quantum limit (the short noise limit) of the signal detection is obtained.