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arXiv:cs/0511070

A particle can carry more than one bit of information

Arindam Mitra

Published Nov 18, 2005• 1 citation
arXivHTMLPDF

Abstract

It is believed that a particle cannot carry more than one bit of information. It is pointed out that particle or single-particle quantum state can carry more than one bit of information. It implies that minimum energy cost of transmitting a bit will be less than the accepted limit KTlog2.
DOI
10.48550/arxiv.cs/0511070

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The elementary particle of information used by modern digital computers is the bit—a register or memory element that can be in one of two distinct states, 0 or 1. But we live in a quantum world, and one can design computers in which each elementary unit of information is a quantum bit, or qubit, which can be in any superposition of two quantum states, |0〉 and |1〉. A quantum computer built with n such components could itself be in a superposition of 2n distinct states, each splinter of the superposition performing its own computation in parallel with all the rest.
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It is known that there is no possibility of transmitting information without a certain amount of energy. This is arbitrarily small in Classical Physics, due to the continuous nature of the energy parameter, while one cannot reduce that amount below Planck's energy quanta in Quantum Physics. In short, one cannot send less than a photon from a place to another when transmitting a minimum of information. However, as single photons are never completely defined simultaneously in all their parameters as position and momentum, their exact contribution to the information transmitted cannot be known in advance, but only probabilistically predicted. So the information transmitted is always blurred before one can - in a way that is only probabilistically predictable - localize or, alternatively, determine the momenta of the photons transporting it. In order to enhance the information content of a message, is it then really possible to exploit the situation by considering the information contained in a superposition state before localization or, alternatively, determination of momenta? It would be so if such blurred information were richer than a defined one, the former being vaguer than the latter as it would be compatible with more possible outputs, and only in this sense more extensive. But if one defines the information content of a state as the negative logarithm of the probability of the state itself, it is not possible to identify the more a priori probable blurred information pertaining to that state with the bigger one. Then the idea of exploiting a supposedly enhanced information content of superposition states in Quantum Computation seems to contradict directly - but, as we will se, without necessity - the classical probabilistic definition of information.