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

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40 Citations (Scopus)
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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
Issue number16
Publication statusPublished - 15 Oct 2015


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


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