Transformation of spin in quantum reference frames

Marion Mikusch (Corresponding author), Luis C. Barbado (Corresponding author), Časlav Brukner (Corresponding author)

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Abstract

In physical experiments, reference frames are standardly modeled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical system that ultimately behaves according to quantum mechanics. We develop a framework for rotational (i.e., spin) quantum reference frames, with respect to which quantum systems with spin degrees of freedom are described. We give an explicit model for such frames as systems composed of three spin coherent states of angular momentum j and introduce the transformations between them by upgrading the Euler angles occurring in classical SO(3) spin transformations to quantum mechanical operators acting on the states of the reference frames. To ensure that an arbitrary rotation can be applied on the spin we take the limit of infinitely large j, in which case the angle operator possesses a continuous spectrum. We prove that rotationally invariant Hamiltonians (such as that of the Heisenberg model) are invariant under a larger group of quantum reference frame transformations. Our result is a development of the quantum reference frame formalism for a non-Abelian group.

Original languageEnglish
Article number043138
Number of pages12
JournalPhysical Review Research
Volume3
Issue number4
DOIs
Publication statusPublished - 29 Nov 2021

Austrian Fields of Science 2012

  • 103025 Quantum mechanics
  • 103028 Theory of relativity

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