Quantum Hilbert hotel

Václav Potoček, Filippo M. Miatto, Mohammad Mirhosseini, Omar S. Magaña-Loaiza, Andreas C. Liapis, Daniel K. L. Oi, Robert W. Boyd, John Jeffers

Research output: Contribution to journalArticle

27 Citations (Scopus)
89 Downloads (Pure)

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.

Original languageEnglish
Article number160505
Number of pages5
JournalPhysical Review Letters
Volume115
Issue number16
DOIs
Publication statusPublished - 15 Oct 2015

Keywords

  • David Hilbert
  • orbital angular momentum
  • paraxial field
  • Hilbert's hotel paradox

Profiles

Projects

Activities

  • 3 Invited talk

The Quantum Hilbert Hotel

Daniel Oi (Speaker)

16 Dec 2015

Activity: Talk or presentation typesInvited talk

Quantum Hilbert Hotel, Quantum CubeSats

Daniel Oi (Speaker)

10 Nov 2015

Activity: Talk or presentation typesInvited talk

The Quantum Hilbert Hotel

Daniel Oi (Speaker)

1 Jul 2015

Activity: Talk or presentation typesInvited talk

Cite this

Potoček, V., Miatto, F. M., Mirhosseini, M., Magaña-Loaiza, O. S., Liapis, A. C., Oi, D. K. L., Boyd, R. W., & Jeffers, J. (2015). Quantum Hilbert hotel. Physical Review Letters, 115(16), [160505]. https://doi.org/10.1103/PhysRevLett.115.160505