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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 continuousvariable 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 nonGaussian 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 

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
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Dive into the research topics of 'Quantum Hilbert hotel'. Together they form a unique fingerprint.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)
16 Dec 2015Activity: Talk or presentation types › Invited talk

Quantum Hilbert Hotel, Quantum CubeSats
Daniel Oi (Speaker)
10 Nov 2015Activity: Talk or presentation types › Invited talk

The Quantum Hilbert Hotel
Daniel Oi (Speaker)
1 Jul 2015Activity: Talk or presentation types › Invited talk