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Journal of Lightwave Technology

Quantum Limits on the Energy Consumption of Optical Transmission Systems

Cristian Antonelli, Antonio Mecozzi, Mark Shtaif, Peter J. Winzer

Published Mar 5, 2014• 14 citations
Publisher

Abstract

The search for schemes that minimize the energy associated with the transmission of information is a longstanding fundamental issue in communication theory. In this paper we extend fundamental limits to the energy consumption per unit of information, as given by Shannon's theory, to the quantum domain. Unlike previous studies, we address a scenario where the signal may be manipulated in an arbitrary way while propagating from the transmitter to the receiver. This situation characterizes many realistic scenarios, such as multi-span fiber-optic communication systems. We obtain the ultimate quantum limit on the energy consumption in this scenario and propose a simple binary energy modulation scheme that approaches this limit within one order of magnitude for practically relevant values of spectral efficiency. Under the same conditions, the quantum energy consumption limit of the standard optically amplified coherent communication scheme is three orders of magnitude above the ultimate identified limit. Throughout the paper we consider transmission of classical information over a quantum channel.

DOI
10.1109/jlt.2014.2309721

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The search for schemes that minimize the energy associated with the transmission of information is a longstanding fundamental issue in communication theory. In this paper we extend fundamental limits to the energy consumption per unit of information, as given by Shannon's theory, to the quantum domain. Unlike previous studies, we address a scenario where the signal may be manipulated in an arbitrary way while propagating from the transmitter to the receiver. This situation characterizes many realistic scenarios, such as multi-span fiber-optic communication systems. We obtain the ultimate quantum limit on the energy consumption in this scenario and propose a simple binary energy modulation scheme that approaches this limit within one order of magnitude for practically relevant values of spectral efficiency. Under the same conditions, the quantum energy consumption limit of the standard optically amplified coherent communication scheme is three orders of magnitude above the ultimate identified limit. Throughout the paper we consider transmission of classical information over a quantum channel.
We consider all-optical networks from a quantum perspective. We show that optimal quantum receivers allow a∼57\sim 57∼57% decrease in energy consumption of all-optical amplifiers. Furthermore, we prove that quantum receivers allow for a logarithmic scaling of the system capacity with the number of pulses per second, while standard Shannon-type systems are limited by the transmit power. Based on our findings we argue for a new approach to optical communication network design, wherein in-line amplifiers are operated at very low gains and in conjunction with high-spectral-bandwidth fiber and a quantum receiver, enhancing data transmission in a practically relevant quantum limit.
This tutorial reviews the Holevo capacity limit as a universal tool to analyze the ultimate transmission rates in a variety of optical communication scenarios, ranging from conventional optically amplified fiber links to free-space communication with power-limited optical signals. The canonical additive white Gaussian noise model is used to describe the propagation of the optical signal. The Holevo limit exceeds substantially the standard Shannon limit when the power spectral density of noise acquired in the course of propagation is small compared to the energy of a single photon at the carrier frequency per unit time-bandwidth area. General results are illustrated with a discussion of efficient communication strategies in the photon-starved regime.
Born about a century ago, Quantum Mechanics has revolutionized the description and the interpretation of Physics at sub-microscopic level. In the last decades, due to the influence of mathematical and engineering research fields, Quantum Mechanics has given birth to related research areas like Quantum Computation, Quantum Information and Quantum Communication. With the discovery of the laser, and later the development of fiber optics and satellite networks, Quantum Communication and Quantum Optics seems to have a natural field of application in Communication Systems. Despite this, the interest in this technology and studies for communication purpose has been overshadowed by the great results in communication networks achieved in the last decades with classical paradigms. However, due to the increasing demand of communication data rate, system designers are now looking at Quantum Mechanics for new and more performanting solutions in communication purposes. Early theoretical studies on Quantum Discrimination Theory and Quantum Information predict better performance for Communication Systems that take advantage of the quantum laws. In addition, Quantum Mechanics provides the deepest description of the physical phenomena, and there are scenarios where a quantum model fits best, as in in deep space communications, where the received signal is really weak, or in a satellite networks, where we are interested in strongly reducing the power of transmitted signals, possibly without sacrificing performance significantly. However, if on one side Quantum Communication Theory promises great gains in the performance of communication systems, on the other hand it fails to describe how to implement physical devices that reach these ultimate limits. So far, only a few architectures achieving these performances are known, and only for simple modulation formats. We are interested in the scenario of optical communications, where the message transmitted is encoded in a sequence of coherent states. Transmitter devices for coherent modulation are well known and consist in laser pulse generators. Instead, receiver implementations working at the quantum limit performance limit are yet to be found. In this Thesis I deal with different topics in the quantum transmission scenario. First, I review existing classical (suboptimal) and quantum (suboptimal and optimal) receiver schemes for the binary coherent modulation. I present a new formulation of the optimal scheme known as Dolinar Receiver with the multiple copies problem, focusing on the information gained during the measurement. Second, I analyze the binary communication in a noisy environment, studying the error probability and the capacity of the binary channel induced. Given the description of the quantum channel, I optimize both the transmitted quantum states and the measurement operators employed in the communication. Third, I consider the Pulse Position Modulation, that is particularly suitable for space and satellite communication due to its simplicity of implementation and high capacity. I review some known suboptimal receivers, and I propose a receiver scheme which approaches the limit performance predicted with quantum theory outperforming the existing schemes. To sum up the results of this Thesis, in order to approach the limit performance predicted by Quantum Mechanics, an optimization is always necessary to exceed the classical effects and trigger the quantum phenomena. In particular, the information gained during the measurement plays an important role, for example in the definition of adaptive receivers. In this Thesis both these aspects have been deeply investigated.
Abstract Quantum communication is an important branch of quantum information science, promising unconditional security to classical communication and providing the building block of a future large-scale quantum network. Noise in realistic quantum communication channels imposes fundamental limits on the communication rates of various quantum communication tasks. It is therefore crucial to identify or bound the quantum capacities of a quantum channel. Here, we consider Gaussian channels that model energy loss and thermal noise errors in realistic optical and microwave communication channels and study their various quantum capacities in the energy-constrained scenario. We provide improved lower bounds to various energy-constrained quantum capacities of these fundamental channels and show that higher communication rates can be attained than previously believed. Specifically, we show that one can boost the transmission rates of quantum information and private classical information by using a correlated multi-mode thermal state instead of the single-mode thermal state of the same energy.
Quantum communication is an important branch of quantum information science, promising unconditional security to classical communication and providing the building block of a future large-scale quantum network. Noise in realistic quantum communication channels imposes fundamental limits on the communication rates of various quantum communication tasks. It is therefore crucial to identify or bound the quantum capacities of a quantum channel. Here, we consider Gaussian channels that model energy loss and thermal noise errors in realistic optical and microwave communication channels and study their various quantum capacities in the energy-constrained scenario. We provide improved lower bounds to various energy-constrained quantum capacities of these fundamental channels and show that higher communication rates can be attained than previously believed. Specifically, we show that one can boost the transmission rates of quantum information and private classical information by using a correlated multi-mode thermal state instead of the single-mode thermal state of the same energy.
A crucial step towards the 6th generation (6G) of networks would be a shift in communication paradigm beyond the limits of Shannon’s theory. In both classical and quantum Shannon’s information theory, communication channels are generally assumed to combine throughclassical trajectories, so that the associated network path traversed by the information carrier is well-defined. Counter-intuitively, quantum mechanics enables a quantum information carrier to propagate through aquantum path, i.e., through a path such that the causal order of the constituting communications channels becomes indefinite. Quantum paths exhibit astonishing features, such as providing non-null capacity even when no information can be sent through any classical path. In this paper, we study the quantum capacity achievable via a quantum path and establish upper and the lower bounds for it. Our findings reveal the substantial advantage achievable with a quantum path over any classical placements of communications channels in terms of ultimate achievable communication rates. Furthermore, we identify the region where a quantum path incontrovertibly outperforms the amount of transmissible information beyond the limits of conventional quantum Shannon’s theory, and we quantify this advantage over classical paths through a conservative estimate.