Projects per year

### 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 language | English |
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Article number | 160505 |

Number of pages | 5 |

Journal | Physical Review Letters |

Volume | 115 |

Issue number | 16 |

DOIs | |

Publication status | Published - 15 Oct 2015 |

### Keywords

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

## Profiles

## Projects

- 1 Finished

## Quantum Digital Signatures

EPSRC (Engineering and Physical Sciences Research Council)

9/02/09 → 8/08/12

Project: Research

## Activities

- 3 Invited talk

## The Quantum Hilbert Hotel

Daniel Oi (Speaker)

Activity: Talk or presentation types › Invited talk

## Quantum Hilbert Hotel, Quantum CubeSats

Daniel Oi (Speaker)

Activity: Talk or presentation types › Invited talk

## The Quantum Hilbert Hotel

Daniel Oi (Speaker)

Activity: Talk or presentation types › Invited talk

## Cite this

*Physical Review Letters*,

*115*(16), [160505]. https://doi.org/10.1103/PhysRevLett.115.160505