title: 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 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.
authors.affiliation: SUPA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom.|Department of Physics, Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Břehová 7, 115 19 Praha 1, Czech Republic.
authors.forename: Václav
authors.initials: V
authors.lastname: Potoček
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada.|Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada.
authors.forename: Filippo M
authors.initials: FM
authors.lastname: Miatto
authors.affiliation: The Institute of Optics, University of Rochester, 500 Joseph C. Wilson Boulevard, Rochester, New York 14627, USA.
authors.forename: Mohammad
authors.initials: M
authors.lastname: Mirhosseini
authors.affiliation: The Institute of Optics, University of Rochester, 500 Joseph C. Wilson Boulevard, Rochester, New York 14627, USA.
authors.forename: Omar S
authors.initials: OS
authors.lastname: Magaña-Loaiza
authors.affiliation: The Institute of Optics, University of Rochester, 500 Joseph C. Wilson Boulevard, Rochester, New York 14627, USA.
authors.forename: Andreas C
authors.initials: AC
authors.lastname: Liapis
authors.affiliation: SUPA Department of Physics, University of Strathclyde, Glasgow G4 0NG, United Kingdom.
authors.forename: Daniel K L
authors.initials: DK
authors.lastname: Oi
authors.affiliation: SUPA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom.|Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada.|The Institute of Optics, University of Rochester, 500 Joseph C. Wilson Boulevard, Rochester, New York 14627, USA.
authors.forename: Robert W
authors.initials: RW
authors.lastname: Boyd
authors.affiliation: SUPA Department of Physics, University of Strathclyde, Glasgow G4 0NG, United Kingdom.
authors.forename: John
authors.initials: J
authors.lastname: Jeffers