Relativistic Quantum Reference Frames: The Operational Meaning of Spin.

Area of Science:

• Quantum Information Science
• Relativistic Quantum Mechanics
• Spin Physics

Background:

• The spin qubit is a fundamental unit in quantum computing.
• Operational spin definition is well-established in the nonrelativistic limit via the Stern-Gerlach setup.
• A relativistic operational definition of spin is currently lacking due to spin-momentum entanglement in boosted frames.

Purpose of the Study:

• To establish an operational definition for spin measurements in the relativistic regime.
• To overcome challenges posed by spin-momentum entanglement in Lorentz-boosted frames.
• To enable quantum information processing with spin qubits under special relativity.

Main Methods:

• Developed a quantum reference frame transformation using a "superposition of Lorentz boosts."
• Transformed to the rest frame of a particle in a superposition of relativistic momenta.
• Defined spin measurements in the particle's rest frame using the Stern-Gerlach procedure.
• Transformed back to the laboratory frame to define relativistic Stern-Gerlach measurements.

Main Results:

• Successfully defined a set of "relativistic Stern-Gerlach measurements" in the laboratory frame.
• Identified observables that satisfy the spin su(2) algebra in the relativistic context.
• Demonstrated a concrete method for testing relativistic spin features.

Conclusions:

• The proposed quantum reference frame transformation provides an operational framework for relativistic spin measurements.
• This work paves the way for quantum information protocols utilizing spin qubits in the special-relativistic domain.
• The findings bridge the gap between quantum information and relativistic quantum mechanics for spin systems.