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IEEE International Symposium on Information Theory (ISIT)

Minimum energy in information transmission

Lev B. Levitin

Published Nov 22, 2002• 0 citations
Publisher

Abstract

It is shown that the minimum energy required to transmit a natural unit of information (nat) over a noisy channel is kT, where T is the effective noise temperature which depends on the interaction between the information career and the environment. The result follows from the entropy defect principle and general laws of quantum dynamics without any specific assumptions.

DOI
10.1109/isit.1997.613157

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It is shown that the minimum energy required to transmit a natural unit of information (nat) over a noisy channel is kT, where T is the effective noise temperature which depends on the interaction between the information career and the environment. The result follows from the entropy defect principle and general laws of quantum dynamics without any specific assumptions.
The literature describing the energy needs for a communications channel has been dominated by analyses of linear electromagnetic transmission, often without awareness that this is a special case. This case leads to the conclusion that an amount of energy equal to kTln 2, where kT is the thermal noise per unit bandwidth, is needed to transmit a bit, and more if quantized channels are used with photon energies hnu > kT. Alternative communication methods are proposed to show that there is no unavoidable minimal energy requirement per transmitted bit. These methods are invoked as part of an analysis of ultimate limits and not as practical procedures.
Energy transfer and information transmission are two fundamental aspects of nature. They are seemingly unrelated, while recent findings suggest that a deep connection between them is to be discovered. This amounts to asking: Can we phrase the processes of transmitting classical bits equivalently as specific energy-transmitting tasks, thereby uncovering foundational links between them? We answer this question positively by showing that, for a broad class of classical communication tasks, a quantum dynamics' ability to transmit n bits of classical information is equivalent to its ability to transmit n units of energy in a thermodynamic task. This finding not only provides an analytical correspondence between information transmission and energy extraction tasks, but also quantifies classical communication by thermodynamics. Furthermore, our findings uncover the dynamical version of Landauer's principle, showing the strong link between transmitting information and energy. In the asymptotic regime, our results further provide thermodynamic meanings for the well-known Holevo-Schumacher-Westmoreland theorem in quantum communication theory.
The optimal rate at which information can be sent through a quantum channel when the transmitted signal must simultaneously carry some minimum amount of energy is characterized. To do so, we introduce the quantum-classical analog of the capacity-power function, and we generalize results in classical information theory for transmitting classical information through noisy channels. We show that the capacity-power function for a classical-quantum channel, for both unassisted and private protocol, is concave, and we also prove additivity for unentangled and uncorrelated ensembles of input signals for such channels. This implies that we do not need regularized formulas for calculation. We show that these properties also hold for all noiseless channels when we restrict the set of input states to be pure quantum states. For general channels, we geometrically prove that the capacity-power function is piecewise concave, with further support from numerical simulations. Further, we connect channel capacity to properties of random quantum states. In particular, we obtain analytical expressions for the capacity-power function for the case of noiseless channels using properties of random quantum states under an energy constraint and concentration phenomena in large Hilbert spaces.
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.
In most communication scenarios, sending a symbol encoded in a quantum state requires spending resources such as energy, which can be quantified by a cost of communication. A standard approach in this context is to quantify the performance of communication protocol by classical capacity, quantifying the maximal amount of information that can be transmitted through a quantum channel per single use of the channel. However, different figures of merit are also possible and a particularly well-suited one is the classical capacity per unit cost, which quantifies the maximal amount of information that can be transmitted per unit cost. I generalize this concept to account for the quantum nature of the information carriers and communication channels and show that if there exists a state with cost equal to zero, e.g., a vacuum state, the capacity per unit cost can be expressed by a simple formula containing maximization of the relative entropy between two quantum states. This enables me to analyze the behavior of photon information efficiency for general communication tasks and show simple bounds on the capacity per unit cost in terms of quantities familiar from quantum estimation theory. I calculate also the capacity per unit cost for general Gaussian quantum channels.