Relative subsystems and quantum reference frame transformations

Area of Science:

• Quantum Information Theory
• Theoretical Physics
• Quantum Foundations

Background:

• Efforts to generalize reference frame transformations to the quantum domain are ongoing.
• A complete theoretical understanding of quantum reference frame transformations remains elusive.

Purpose of the Study:

• To derive general quantum reference frame transformations from first principles using standard quantum theory.
• To develop a framework that provides a more complete understanding of these transformations.

Main Methods:

• Derivation of transformations based on incoherent group averaging.
• Application of standard quantum theory principles.
• Analysis of symmetry groups and their quantum generalizations.

Main Results:

• A general framework for quantum reference frame transformations applicable to a broad range of symmetry groups.
• Reversible transformations dependent only on reference frames and the system of interest.
• Identification of an
• extra particle
• carrying quantum information about reference frame states.
• More general transformations than previously found, not restricted to a specific subspace.

Conclusions:

• The proposed framework offers a more comprehensive understanding of quantum reference frame transformations.
• The inclusion of an
• extra particle
• reveals new quantum features of reference frames.
• The framework provides key insights, particularly when applied to the centrally extended Galilei group.