Abstract
Before studying the new aspects that quantum mechanics adds to information theory below, we will have a brief look at the basics of classical information theory in the next section. Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information.
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Notes
- 1.
As is well known [9], in 1961, Landauer had the important insight that there is a fundamental asymmetry in nature that allows us to process information. Copying classical information can be done reversibly and without wasting any energy, but when information is erased there is always an energy cost of kT ln 2 per classical bit to be paid ( for more details see, also [36]). Furthermore, an amount of heat equal to kT ln 2 is damped in the environment at the end of the erasing process. Landauer conjectured that this energy/entropy cost cannot be reduced below this limit irrespective of how the information is encoded and subsequently erased—it is a fundamental limit. Landauer’s discovery is important both theoretically and practically, as on the one hand, it relates the concept of information to physical quantities like thermodynamical entropy and free energy, and on the other hand, it may force the future designers of quantum devices to take into account the heat production caused by the erasure of information although this effect is tiny and negligible in today’s technology. At the same time, Landauer’s profound insight has led to the resolution of the problem of Maxwell’s demon by Bennett [37, 38]. By the way, for the first time the physical relation between entropy and information was done by Szilard at the investigation of the task of the Maxwell’s demon [30, 31]. On the other hand, mathematical definition of the information was introduced by Hartley in 1928 [11] and more elaboration on this definition was done by Shannon [1].
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Plekhanov, V.G. (2012). Classical and Quantum Information. In: Isotope-Based Quantum Information. SpringerBriefs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28750-3_3
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