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

Frontiers in Optics

Information Capacities of Linear Time-Invariant Bosonic Channels with Additive Gaussian Noise

Jacob M. Leamer, Chenglong You, Bhaskar Roy Bardhan

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We investigate various information capacities of linear time invariant quantum bosonic channels representing amplification and attenuation in optical fiber communications. We compare these capacities with those of optical coherent detection.
DOI
10.1364/fio.2017.jw4a.34

Related papers

Ultimate capacity of linear time-invariant bosonic channels with additive Gaussian noise

Bhaskar Roy Bardhan, Jeffrey H. Shapiro

Fiber-optic communications are moving to coherent detection in order to increase their spectral efficiency, i.e., their channel capacity per unit bandwidth. At power levels below the threshold for significant nonlinear effects, the channel model for such operation a linear time-invariant filter followed by additive Gaussian noise is one whose channel capacity is well known from Shannon's noisy channel coding theorem. The fiber channel, however, is really a bosonic channel, meaning that its ultimate classical information capacity must be determined from quantum-mechanical analysis, viz. from the Holevo-Schumacher-Westmoreland (HSW) theorem. Based on recent results establishing the HSW capacity of a linear (lossy or amplifying) channel with additive Gaussian noise, we provide a general continuous-time result, namely the HSW capacity of a linear time-invariant (LTI) bosonic channel with additive Gaussian noise arising from a thermal environment. In particular, we treat quasi-monochromatic communication under an average power constraint through a channel comprised of a stable LTI filter that may be attenuating at all frequencies or amplifying at some frequencies and attenuating at others. Phase-insensitive additive Gaussian noise-associated with the continuous-time Langevin noise operator needed to preserve free-field commutator brackets is included at the filter output. We compare the resulting spectral efficiencies with corresponding results for heterodyne and homodyne detection over the same channel to assess the increased spectral efficiency that might be realized with optimum quantum reception.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 15, 2016•0 citations

Evaluating capacities of bosonic Gaussian channels

Alexander Semenovich Holevo, Reinhard F. Werner

We show how to compute or at least to estimate various capacity-related quantities for bosonic Gaussian channels. Among these are the coherent information, the entanglement-assisted classical capacity, the one-shot classical capacity, and a quantity involving the transpose operation, shown to be a general upper bound on the quantum capacity, even allowing for finite errors. All bounds are explicitly evaluated for the case of a one-mode channel with attenuation or amplification and classical noise.

arXiv:quant-ph/9912067•Physical Review A•Feb 1, 2001•576 citations

Ultimate capacity of a linear time-invariant bosonic channel

Bhaskar Roy Bardhan, Jeffrey H. Shapiro

Optical channels play an important role in the information era, in which establishing the ultimate rate for reliably transmitting communication is paramount. Building on recent breakthroughs, the authors derive the capacity of quantum channels including realistic processes, providing a direct link to practical broadband communications schemes.

arXiv:1602.03182•Physical Review A•Mar 31, 2016•11 citations

Sending Quantum Information with Gaussian States

Alexander Semenovich Holevo

Quantum information characteristics, such as quantum mutual information, loss, noise and coherent information are explicitly calculated for Bosonic attenuation/amplification channel with input Gaussian state. The coherent information is shown to be negative for the values of the attenuation coefficient \( k < 1\sqrt 2 \).

arXiv:quant-ph/9809022•Kluwer Academic Publishers eBooks•Dec 19, 2005•7 citations

Capacity of optical transmission with attenuation and amplification

Xiaoyu Chen, Li-zhen Jiang, Liang Han

The optical signal transmitted on a fiber with thermal noise, attenuation and amplification is studied. The channel is considered as a quantum channel while the signal to be transmitted is classical. The classical information is encoded in a quantum state then it is transmitted in optical fiber. At the receiving end, measurement is performed on the output quantum state to retrieve the classical information. The optimal distribution of the input quantum state achieving the channel capacity is Gaussian. The capacity is characterized by the attenuation/amplification coefficient and thermal noise in the transmission and at the measurement process together by the power of the input. The loss (or attenuation) of an optical fiber usually should be compensated by the amplification. We show that when they coexist, additional noise occurs

IEEE Information Theory Workshop (ITW)•Oct 1, 2006•0 citations

Classical Capacity of Single-Mode Bosonic Gaussian Channels

Gerardo Adesso, Ludovico Lami, Vittorio Giovannetti

The classical capacity of a noisy optical channel is the maximum rate at which information can be transmitted reliably, given a constraint on the mean input energy. For the ubiquitous bosonic Gaussian channels, which include standard models of loss and noise in fibre and free-space optical links, determining this rate requires addressing whether entanglement between channel uses or non-Gaussian signals can outperform Gaussian encodings. More precisely, the question is whether the energy-constrained Holevo information is additive across arbitrarily many channel uses and coincides with its Gaussian counterpart. We answer these fundamental questions in the affirmative for every single-mode bosonic Gaussian channel at every input energy. Namely, we prove that independently prepared Gaussian states with Gaussian-distributed random displacements achieve the capacity, including in the low-energy regime where squeezing the signals competes with encoding information in their displacement. Our proof connects an entanglement inequality to a sharp, additive lower bound on output entropy. We then characterise communication above capacity: under a strict total photon-number cutoff, the probability of correct decoding decreases exponentially with the number of channel uses, and we derive explicit bounds on the decay exponent. When only the mean photon number is constrained, a simple energy-rescaling formula determines exactly the entire asymptotic rate--error trade-off: the capacity at mean photon number $N$ and allowed average decoding error $ε$ equals the vanishing-error capacity at mean photon number $N/(1-ε)$. Together, these results identify the ultimate limits of classical communication for some of the most fundamental models of optical communication.

quant-pharXiv:2610.22308•Oct 16, 2026•0 citations
Fiber-optic communications are moving to coherent detection in order to increase their spectral efficiency, i.e., their channel capacity per unit bandwidth. At power levels below the threshold for significant nonlinear effects, the channel model for such operation a linear time-invariant filter followed by additive Gaussian noise is one whose channel capacity is well known from Shannon's noisy channel coding theorem. The fiber channel, however, is really a bosonic channel, meaning that its ultimate classical information capacity must be determined from quantum-mechanical analysis, viz. from the Holevo-Schumacher-Westmoreland (HSW) theorem. Based on recent results establishing the HSW capacity of a linear (lossy or amplifying) channel with additive Gaussian noise, we provide a general continuous-time result, namely the HSW capacity of a linear time-invariant (LTI) bosonic channel with additive Gaussian noise arising from a thermal environment. In particular, we treat quasi-monochromatic communication under an average power constraint through a channel comprised of a stable LTI filter that may be attenuating at all frequencies or amplifying at some frequencies and attenuating at others. Phase-insensitive additive Gaussian noise-associated with the continuous-time Langevin noise operator needed to preserve free-field commutator brackets is included at the filter output. We compare the resulting spectral efficiencies with corresponding results for heterodyne and homodyne detection over the same channel to assess the increased spectral efficiency that might be realized with optimum quantum reception.
We show how to compute or at least to estimate various capacity-related quantities for bosonic Gaussian channels. Among these are the coherent information, the entanglement-assisted classical capacity, the one-shot classical capacity, and a quantity involving the transpose operation, shown to be a general upper bound on the quantum capacity, even allowing for finite errors. All bounds are explicitly evaluated for the case of a one-mode channel with attenuation or amplification and classical noise.
Quantum information characteristics, such as quantum mutual information, loss, noise and coherent information are explicitly calculated for Bosonic attenuation/amplification channel with input Gaussian state. The coherent information is shown to be negative for the values of the attenuation coefficient k<12 k < 1\sqrt 2 k<12​.
The optical signal transmitted on a fiber with thermal noise, attenuation and amplification is studied. The channel is considered as a quantum channel while the signal to be transmitted is classical. The classical information is encoded in a quantum state then it is transmitted in optical fiber. At the receiving end, measurement is performed on the output quantum state to retrieve the classical information. The optimal distribution of the input quantum state achieving the channel capacity is Gaussian. The capacity is characterized by the attenuation/amplification coefficient and thermal noise in the transmission and at the measurement process together by the power of the input. The loss (or attenuation) of an optical fiber usually should be compensated by the amplification. We show that when they coexist, additional noise occurs
The classical capacity of a noisy optical channel is the maximum rate at which information can be transmitted reliably, given a constraint on the mean input energy. For the ubiquitous bosonic Gaussian channels, which include standard models of loss and noise in fibre and free-space optical links, determining this rate requires addressing whether entanglement between channel uses or non-Gaussian signals can outperform Gaussian encodings. More precisely, the question is whether the energy-constrained Holevo information is additive across arbitrarily many channel uses and coincides with its Gaussian counterpart. We answer these fundamental questions in the affirmative for every single-mode bosonic Gaussian channel at every input energy. Namely, we prove that independently prepared Gaussian states with Gaussian-distributed random displacements achieve the capacity, including in the low-energy regime where squeezing the signals competes with encoding information in their displacement. Our proof connects an entanglement inequality to a sharp, additive lower bound on output entropy. We then characterise communication above capacity: under a strict total photon-number cutoff, the probability of correct decoding decreases exponentially with the number of channel uses, and we derive explicit bounds on the decay exponent. When only the mean photon number is constrained, a simple energy-rescaling formula determines exactly the entire asymptotic rate--error trade-off: the capacity at mean photon number NNN and allowed average decoding error εεε equals the vanishing-error capacity at mean photon number N/(1−ε)N/(1-ε)N/(1−ε). Together, these results identify the ultimate limits of classical communication for some of the most fundamental models of optical communication.