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Shannon’s Information and Heisenberg’s Uncertainty

Robert H. McEachern

Published Mar 1, 2020• 0 citations
OpenAlex

Abstract

It is shown that the least possible amount of Shannon’s information (a single bit) corresponds to the least possible value of the Heisenberg Uncertainty Principle.

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The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy. Independently, due to quantum gravity effects the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP). In this work, we show that GUP has been derived from considering non-extensive entropies, proposed by one of us. We found that the deformation parameters associated with S+ and S− entropies are negative and positive respectively. This allows us to explore various possibilities in the search of physical implications. We conclude that non-extensive statistics constitutes a signature of quantum gravity.
Abstract Landauer’s bound is applicable to irreversible quantum operations. In this study, we showcased that the Doppler temperature manifests the existence of Landauer’s bound, which does not block a spin from (irreversibly) flipping with a tiny amount of energy via quantum tunneling. Verified by a spin–spin magnetic interaction experiment, this (energy) amount was determined to be only 1.25 times the theoretical value of Landauer’s bound. Based on Heisenberg’s principle, we defined information from a measuring perspective: one bit of information corresponds to the smallest error when quantifying the product of the measured energy uncertainty ( ΔE\Delta EΔE Δ E ) and the measured time duration ( Δt\Delta tΔt Δ t ). We then illustrate an optically manipulated, spin-encoded, near-Landauer-bound, near-Heisenberg-limit quantum computer that encompasses this new definition of information. This study may represent the last piece of the puzzle in understanding both quantum Landauer erasure and Heisenberg’s quantum limit since a single spin is the smallest information carrier.