Physikalische und biologische Grenzen der Informationsübermittlung

Marko, Hans

doi:10.1007/bf00274090

Cited by 29 publications

(6 citation statements)

References 5 publications

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“…This suggests that long signals must also obey a Pendry type formula, albeit approximately. Indeed, long ago Marko 6 proposed that I max ∝ (Eτ /h) 1/2 for long duration signals. As we shall see in Sec.3.4., for ξ = Eτ /h ∼ > 100, ℑ(ξ) → B √ ξ.…”

Section: General Form Of Bound On Burst Communicationmentioning

confidence: 99%

“…We shall express all this in equations in Sec.2. 6 Shannon's entropy formula (1) parallels Boltzmann's definition of entropy as used in the proof of the H theorem. (This explains the use of the name "entropy" and the symbol H in information theory, both suggested to Shannon by von Neumann.…”

Section: Shannon's Information Theorymentioning

confidence: 99%

“…Some aspects of the spacetime view of information are described in Sec. 6. New here are discussions of the influence of signal self-gravitation on communication, and of the role of acceleration as a jammer of information transfer.…”

Section: Introductionmentioning

confidence: 99%

“…Early expressions of an approximate nature for quantum capacity were proposed by Stern, 3 Gordon, 4,5 and Marko. 6 In 1963 Lebedev and Levitin 7 , starting from thermodynamic considerations, obtained a precise and powerful formula for channel capacity including the effects of both quantum and thermal noise. In the classical limit this formula reduces to Shannon's, while in the noiseless limit it leads back to the estimate of Stein and Gordon [see Eq.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Limitations on the Storage and Transmission of Information

Bekenstein

Schiffer²

1990

Int. J. Mod. Phys. C

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Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are here described. Quantum channel capacity theory is reviewed for both steady state and burst communication. An analytic approximation is given for the maximum signal information possible with occupation number signal states as a function of mean signal energy. A theorem guaranteeing that these states are optimal for communication is proved. A heuristic "proof" of the linear bound on communication is given, followed by rigorous proofs for signals with specified mean energy, and for signals with given energy budget. And systems of many parallel quantum channels are shown to obey the linear bound for a natural channel architecture. The time-energy uncertainty principle is reformulated in information language by means of the linear bound. The quantum bound on information storage capacity of quantum mechanical and quantum field devices is reviewed. A simplified version of the analytic proof for the bound is given for the latter case. Solitons as information caches are discussed, as is information storage in one dimensional systems. The influence of signal self-gravitation on communication is considerd. Finally, it is shown that acceleration of a receiver acts to block information transfer.

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Section: General Form Of Bound On Burst Communicationmentioning

confidence: 99%

Section: Shannon's Information Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum Limitations on the Storage and Transmission of Information

Bekenstein

Schiffer²

1990

Int. J. Mod. Phys. C

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“…Winograd's limits, lower bounds on the time for arithmetic operations, are one kind. Physically, using the idea that the unit of energy required to switch from one state to another is kT In, 2, Landauer [17], Marko [30], and others observe that there are something like 1093 bits available for information from all of the mass of the universe. The maximum rate at which these might be processed has been calculated by Bremermann [31] to be 1047 bits per gram per sec.…”

mentioning

confidence: 99%

Mathematical applications, computation, and complexity

Cohen¹

1972

Quart. Appl. Math.

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In this lecture I want to discuss some matters which are not themselves applied mathematics but are about the profession and practice of applied mathematics. In the trade, the measures of an article's quality are the sparsity of the prose, the swiftness of the mathematics, and the sweet connection to the real world. This one will be rather thick in prose and sparse in mathematics. I would have liked to have been able to respond to Prof. Davis's invitation to be philosophical, but that has always seemed to be a dangerous way to behave publicly. I offer these comments from the point of view of an industrial mathematician and as one of the Old Browns.When I arrived at Brown nearly twenty-five years ago, the world looked a little different to a young applied mathematician than it does to a middle-aged applied mathematician now. It was clear that what was to be learned at Brown was continuum mechanics and the complex function and differential equation theory that was a part of it. Fluid mechanics, elasticity, plasticity-we were beginning to grapple with those problems that von Karman had said we were to in his 1940 Gibbs lecture [1]. We were really not yet "tooled up" for nonlinearity, as he urged in the first issue of the Quarterly of Applied Mathematics [2], but there was a realization of its importance. There was an atmosphere of the beginning of something at Brown in the late 1940s and, in fact, it was a beginning-a feeling that there were many, many problems to be solved in aerodynamics, flutter and aero-elasticity, viscous flow and boundary layers, plastic design, vibration problems. These were obviously good problems to solve because someone, somewhere needed the solutions, or they were hard, or they were the next problem in their field, or just because they were there. We were (and, of course, I'm aware of that benevolent distortion that occurs in looking backward this way) an optimistic crew who had a great deal of confidence in the results, techniques, and styles of thought of several generations of European applied mathematicians. One can observe that for American science, applied mathematics was a rather new field then, not very populated or popular but with an apparent good potential for growth. Furthermore, when scientists thought of the uses of mathematics, they were used to thinking of the applications of classical analysis to the problems of the physical sciences.In a corner of the house at 27 Brown Street there was a large room full of girls and machines--our computers. It was a small but busy and necessary enterprise. Other important locations were the softball field and the house on Benevolent Street where the Friday afternoon post-colloquium sessions were held.Before nostalgia overcomes, what happened to all of that? Where are we? What I think has happened is that the needs for and uses of mathematics have

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Wideband Quantum Communication: A New Frontier?

Drummond

Caves

1992

Quantum Measurements in Optics

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Physikalische und biologische Grenzen der Informationsübermittlung

Cited by 29 publications

References 5 publications

Quantum Limitations on the Storage and Transmission of Information

Quantum Limitations on the Storage and Transmission of Information

Mathematical applications, computation, and complexity

Wideband Quantum Communication: A New Frontier?

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