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

Quantum noise in optical communication systems

Haiqing Wei, David V. Plant

Published Jan 26, 2004• 1 citation
Publisher

Abstract

It is noted that the fiber propagation loss is a random process along the length of propagation. The stochastic nature of the loss process induces a random fluctuation to the energy of the optical signals, which, as an extra source of noise, could become comparable to the amplified-spontaneous-emission noise of optical amplifiers. The optical noise in random loss/gain has a quantum origin, as a manifestation of the corpuscular nature of electromagnetic radiation. This paper adopts the Schrodinger representation, and uses a density matrix in the basis of photon number states to describe the optical signals and their interaction with the environment of loss/gain media. When the environmental degrees of freedom are traced out, a reduced density matrix is obtained in the diagonal form, which describes the total energy of the optical signal evolving along the propagation distance. Such formulism provides an intuitive interpretation of the quantum-optical noise as the result of a classical Markov process in the space of the photon number states. The formulism would be more convenient for practical engineers, and should be sufficient for fiber-optic systems with direct intensity detection, because the quantity of concern is indeed the number of photons contained in a signal pulse. Even better, the model admits analytical solutions to the photon-number distribution of the optical signals.

DOI
10.1117/12.506472

Related papers

Quantum noise in photonics

CHARLES H. HENRY, Rudolf F. Kazarinov

The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]

Reviews of Modern Physics•Jul 1, 1996•220 citations

Quantum noise figure of fiber OPAs

M.E. Marhic

Introduction In previous chapters we studied wave propagation in fiber OPAs from a classical standpoint, i.e. starting from Maxwell's equations. That approach provides only a partial view of the rich nature of the electromagnetic field, namely its wave nature. However, a complete description of the electromagnetic field requires quantum mechanics. This quantum description of the electromagnetic field (called quantum electrodynamics, or QED) predicts fluctuations in measurable quantities due to the Heisenberg uncertainty principle and sets ultimate limits on the performance of devices such as optical amplifiers. A remarkable result of this theory is that the statistics and thus the noise performance of a system are affected by the quantum statistics of the source and by the physical measurement that is made. Thus a different analysis is needed depending on whether homodyne, heterodyne, or direct detection (where the field simply impinges on a photodiode) is used. Direct detection reveals the particle nature of the electromagnetic field. More specifically, energy arrives in discrete units, called photons, each of which may create an electron–hole pair in a semiconductor photodetector. In particular, the number of photons in an optical pulse can be thought of as a random variable having a mean and a variance. By deriving the mean and variance of the photocurrent that would be present if one performed direct detection of ideal laser light at the input of an optical amplifier and then a similar measurement at its exit, one can quantify the degradation of the signal-to-noise ratio (SNR) caused by the amplifier.

Cambridge University Press eBooks•Nov 15, 2007•0 citations

Origin of quantum noise and decoherence in distributed amplifiers

J. D. Franson, Brian T. Kirby

The use of distributed amplifiers may have some potential advantages for the transmission of quantum information through optical fibers. In addition to the quantum noise introduced by the amplifiers, entanglement between atoms in the amplifying media and the optical field corresponds to which-path information that can further reduce the coherence. Here we analyze the effects of decoherence in a phase-insensitive distributed amplifier by using perturbation theory to calculate the state of the entire system including the atomic media. For an initial coherent state, tracing over the atomic states allows the reduced density matrix of the field to be expressed as a mixture of squeezed states with a reduced spread in photon number and an increased phase uncertainty. The amplifier noise and decoherence can be interpreted as being due to entanglement with the environment rather than the amplification of vacuum fluctuation noise.

arXiv:1502.07761•Physical Review A•Nov 9, 2015•2 citations

Noise properties of propagation through slow- and fast-light media

Robert W. Boyd, Zhimin Shi, Peter W. Milonni

We consider the fundamental noise properties of propagation through slow- and fast-light optical media based on gain or loss processes. For purely quantum mechanical reasons, any gain or loss process will add noise to a transmitted light field. We derive a relation between the noise figure describing the decreased signal-to-noise ratio of the transmitted laser pulse and the fractional delay or advancement of the pulse. We apply these results explicitly to the situation of operation on the line center of a gain or loss line. We find that for an ideal gain medium the noise figure never exceeds a factor of two. For a loss medium, there is no limit as to how large the noise figure can become. The increased noise in this case is the result of the random loss of photons from the optical field.

Journal of Optics•Sep 24, 2010•16 citations

Quantum theory of a saturable optical amplifier

N. B. Abraham

The intensity fluctuations in the output of a saturable optical amplifier are studied as the amplifier length is increased. Characteristics are determined by calculation of the diagonal elements of the density matrix of the optical field. Saturation affecting both upper-state and lower-state atomic populations is considered. Spontaneous emission distributed along the amplifier causes the "photon-number" distribution to approach a Bose-Einstein distribution during linear amplification if the input field is not Bose-Einstein. The onset of saturation reduces the relative fluctuations of the optical field both by introducing nonlinear gain and by reducing the spontaneous emission. Limiting solutions show that strong saturation leads to a major reduction in the fluctuations causing the photon-number distribution to approach a Poisson distribution.

Physical Review A•May 1, 1980•12 citations

Photon noise

H. A. Haus, J. A. Mullen

Two types of noise are discussed that may become important when light frequencies are used for communication purposes. At such high frequencies a quantum of energy is not negligible compared to the total transmitted energies (low number of quanta!). The fluctuations caused by the nonzero size of a quantum of energy will predominate over thermal noise, and the usual amplifier noise encountered at microwave (and lower) frequencies. The two types of processes producing quantum noise that we intend to discuss are shown in Pig. 1. They are: The radiative attenuation noise introduced when a signal, phase-and amplitude-control1ed at the high-power transmitter end, is highly attenuated through the inverse square law radiative attenuation. Such a process would take place in the use of optical frequencies for energy transmission over large distances. The noise introduced in linear amplification. objective of this paper is to show how these forms of noise can be analyzed using simple statistics and classical electromagnetic theory with the aid of only a few quantum-theoretical results that have a simple physical meaning.

Microwaves•Jan 1, 1963•0 citations
It is noted that the fiber propagation loss is a random process along the length of propagation. The stochastic nature of the loss process induces a random fluctuation to the energy of the optical signals, which, as an extra source of noise, could become comparable to the amplified-spontaneous-emission noise of optical amplifiers. The optical noise in random loss/gain has a quantum origin, as a manifestation of the corpuscular nature of electromagnetic radiation. This paper adopts the Schrodinger representation, and uses a density matrix in the basis of photon number states to describe the optical signals and their interaction with the environment of loss/gain media. When the environmental degrees of freedom are traced out, a reduced density matrix is obtained in the diagonal form, which describes the total energy of the optical signal evolving along the propagation distance. Such formulism provides an intuitive interpretation of the quantum-optical noise as the result of a classical Markov process in the space of the photon number states. The formulism would be more convenient for practical engineers, and should be sufficient for fiber-optic systems with direct intensity detection, because the quantity of concern is indeed the number of photons contained in a signal pulse. Even better, the model admits analytical solutions to the photon-number distribution of the optical signals.
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]
Introduction In previous chapters we studied wave propagation in fiber OPAs from a classical standpoint, i.e. starting from Maxwell's equations. That approach provides only a partial view of the rich nature of the electromagnetic field, namely its wave nature. However, a complete description of the electromagnetic field requires quantum mechanics. This quantum description of the electromagnetic field (called quantum electrodynamics, or QED) predicts fluctuations in measurable quantities due to the Heisenberg uncertainty principle and sets ultimate limits on the performance of devices such as optical amplifiers. A remarkable result of this theory is that the statistics and thus the noise performance of a system are affected by the quantum statistics of the source and by the physical measurement that is made. Thus a different analysis is needed depending on whether homodyne, heterodyne, or direct detection (where the field simply impinges on a photodiode) is used. Direct detection reveals the particle nature of the electromagnetic field. More specifically, energy arrives in discrete units, called photons, each of which may create an electron–hole pair in a semiconductor photodetector. In particular, the number of photons in an optical pulse can be thought of as a random variable having a mean and a variance. By deriving the mean and variance of the photocurrent that would be present if one performed direct detection of ideal laser light at the input of an optical amplifier and then a similar measurement at its exit, one can quantify the degradation of the signal-to-noise ratio (SNR) caused by the amplifier.
The use of distributed amplifiers may have some potential advantages for the transmission of quantum information through optical fibers. In addition to the quantum noise introduced by the amplifiers, entanglement between atoms in the amplifying media and the optical field corresponds to which-path information that can further reduce the coherence. Here we analyze the effects of decoherence in a phase-insensitive distributed amplifier by using perturbation theory to calculate the state of the entire system including the atomic media. For an initial coherent state, tracing over the atomic states allows the reduced density matrix of the field to be expressed as a mixture of squeezed states with a reduced spread in photon number and an increased phase uncertainty. The amplifier noise and decoherence can be interpreted as being due to entanglement with the environment rather than the amplification of vacuum fluctuation noise.
We consider the fundamental noise properties of propagation through slow- and fast-light optical media based on gain or loss processes. For purely quantum mechanical reasons, any gain or loss process will add noise to a transmitted light field. We derive a relation between the noise figure describing the decreased signal-to-noise ratio of the transmitted laser pulse and the fractional delay or advancement of the pulse. We apply these results explicitly to the situation of operation on the line center of a gain or loss line. We find that for an ideal gain medium the noise figure never exceeds a factor of two. For a loss medium, there is no limit as to how large the noise figure can become. The increased noise in this case is the result of the random loss of photons from the optical field.
The intensity fluctuations in the output of a saturable optical amplifier are studied as the amplifier length is increased. Characteristics are determined by calculation of the diagonal elements of the density matrix of the optical field. Saturation affecting both upper-state and lower-state atomic populations is considered. Spontaneous emission distributed along the amplifier causes the "photon-number" distribution to approach a Bose-Einstein distribution during linear amplification if the input field is not Bose-Einstein. The onset of saturation reduces the relative fluctuations of the optical field both by introducing nonlinear gain and by reducing the spontaneous emission. Limiting solutions show that strong saturation leads to a major reduction in the fluctuations causing the photon-number distribution to approach a Poisson distribution.
Two types of noise are discussed that may become important when light frequencies are used for communication purposes. At such high frequencies a quantum of energy is not negligible compared to the total transmitted energies (low number of quanta!). The fluctuations caused by the nonzero size of a quantum of energy will predominate over thermal noise, and the usual amplifier noise encountered at microwave (and lower) frequencies. The two types of processes producing quantum noise that we intend to discuss are shown in Pig. 1. They are: The radiative attenuation noise introduced when a signal, phase-and amplitude-control1ed at the high-power transmitter end, is highly attenuated through the inverse square law radiative attenuation. Such a process would take place in the use of optical frequencies for energy transmission over large distances. The noise introduced in linear amplification. objective of this paper is to show how these forms of noise can be analyzed using simple statistics and classical electromagnetic theory with the aid of only a few quantum-theoretical results that have a simple physical meaning.