Quantum Hilbert Hotel

Authors

Václav Potoček, University of Glasgow
Filippo M. Miatto, University of Waterloo
Mohammad Mirhosseini, University of Rochester Institute of Optics
Omar S. Magaña-Loaiza, University of Rochester Institute of Optics
Andreas C. Liapis, University of Rochester Institute of Optics
Daniel K.L. Oi, University of Strathclyde
Robert W. Boyd, University of Glasgow
John Jeffers, University of Strathclyde

Document Type

Article

Publication Date

10-15-2015

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 realizing 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 NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.

Publication Source (Journal or Book title)

Physical Review Letters

Recommended Citation

Potoček, V., Miatto, F., Mirhosseini, M., Magaña-Loaiza, O., Liapis, A., Oi, D., Boyd, R., & Jeffers, J. (2015). Quantum Hilbert Hotel. Physical Review Letters, 115 (16) https://doi.org/10.1103/PhysRevLett.115.160505