Quantum Galilei group as quantum reference frame transformations
Angel Ballesteros, Diego Fernandez-Silvestre, Flaminia Giacomini, Giulia Gubitosi
Published April 1, 2025 · Updated November 30, 2025
Abstract
Quantum groups have been widely explored as a tool to encode possible nontrivial generalisations of reference frame transformations, relevant in quantum gravity. In quantum information, it was found that the reference frames can be associated to quantum particles, leading to quantum reference frames transformations. The connection between these two frameworks is still unexplored, but if clarified it will lead to a more profound understanding of symmetries in quantum mechanics and quantum gravity. Here, we establish a correspondence between quantum reference frame transformations and transformations generated by a quantum deformation of the Galilei group with commutative time, taken at first order in the quantum deformation parameter. This is found once the quantum group noncommutative transformation parameters are represented on the phase space of a quantum particle, and upon setting the quantum deformation parameter to be proportional to the inverse of the mass of the particle serving as the quantum reference frame. These results allow us to show that quantum reference frame transformations are physically relevant when the state of the quantum reference frame is in a quantum superposition of semiclassical states. We conjecture that the all-order quantum Galilei group describes quantum reference frame transformations between more general quantum states of the quantum reference frame.
Author comment
20 pages + 3 pages Appendix. Version accepted in Quantum
More in quant-ph
- Tianyan: Cloud services with quantum advantageTianyan Quantum Group
- Unifying communication paradigms in measurement-based delegated quantum computingFabian Wiesner, Jens Eisert, Anna Pappa
- Entangling Disciplines: Causality, Entropy and Time-Travel Paradoxes on a Quantum ComputerMaria Violaris
- Classical (ontological) dual states in quantum theory and the minimal group representation Hilbert spaceDiego J. Cirilo-Lombardo, Norma G. Sanchez
- Doubly Quantum MechanicsVittorio D'Esposito, Giuseppe Fabiano, Domenico Frattulillo +1