The Quantum Hilbert Hotel
Abstract
In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of "infinity". In continuous-variable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert's hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realising it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited for example for enhancing the sensitivity of N00N states, for increasing the capacity of a channel or for multiplexing multiple channels into a single one.
Cite
@article{arxiv.1506.00675,
title = {The Quantum Hilbert Hotel},
author = {Václav Potocek and Filippo M. Miatto and Mohammad Mirhosseini and Omar S. Magaña-Loaiza and Andreas C. Liapis and Daniel K. L. Oi and Robert W. Boyd and John Jeffers},
journal= {arXiv preprint arXiv:1506.00675},
year = {2015}
}
Comments
4 figures 5 pages