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.
Publication Source (Journal or Book title)
Physical Review Letters
Potoček, V., Miatto, F., Mirhosseini, M., Magaña-Loaiza, O., Liapis, A., Oi, D., Boyd, R., & Jeffers, J. (2015). Quantum Hilbert Hotel. Physical Review Letters, 115 (16) https://doi.org/10.1103/PhysRevLett.115.160505