Quantum Hilbert Hotel: Endless Possibilities

[DrClaude]

Researchers have created a quantum version of the Hilbert hotel:

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.160505

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.

 

[eljose79]

Thank you for sharing this interesting article about the quantum version of the Hilbert hotel. As a scientist in the field of quantum mechanics, I find this research to be both fascinating and important.

The concept of infinity is a fundamental aspect of mathematics and has been a topic of discussion and debate for centuries. The Hilbert hotel paradox, first proposed by David Hilbert in 1924, is a well-known thought experiment that highlights the counterintuitive nature of infinity.

In this new research, the authors have demonstrated that the principles of quantum mechanics can accommodate a similar paradoxical situation. By using a protocol that maps the amplitudes of an infinite eigenbasis to twice their original quantum number, they were able to create infinitely many unoccupied levels in a coherent and deterministic manner.

This achievement has potential implications in various areas of quantum information science. For example, it could be used to enhance the sensitivity of NOON states, increase the capacity of a channel, or multiplex multiple channels into a single one.

The experimental realization of this protocol on the orbital angular momentum of a paraxial field is a significant step forward in the field of quantum mechanics. It demonstrates the feasibility of this concept and opens up new possibilities for exploring the nature of infinity in the quantum world.

I am eager to see further developments in this area and how this new non-Gaussian operation may be applied in other quantum systems. Thank you for bringing this research to our attention.