Relativistic Quantum Reference Frames: The Operational Meaning of Spin

Flaminia Giacomini, Esteban Castro-Ruiz, and Časlav Brukner
Phys. Rev. Lett. 123, 090404 – Published 29 August 2019
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Abstract

The spin is the prime example of a qubit. Encoding and decoding information in the spin qubit is operationally well defined through the Stern-Gerlach setup in the nonrelativistic (i.e., low velocity) limit. However, an operational definition of the spin in the relativistic regime is missing. The origin of this difficulty lies in the fact that, on the one hand, the spin gets entangled with the momentum in Lorentz-boosted reference frames, and on the other hand, for a particle moving in a superposition of velocities, it is impossible to “jump” to its rest frame, where spin is unambiguously defined. Here, we find a quantum reference frame transformation corresponding to a “superposition of Lorentz boosts,” allowing us to transform to the rest frame of a particle that is in a superposition of relativistic momenta with respect to the laboratory frame. This enables us to first move to the particle’s rest frame, define the spin measurements there (via the Stern-Gerlach experimental procedure), and then move back to the laboratory frame. In this way, we find a set of “relativistic Stern-Gerlach measurements” in the laboratory frame, and a set of observables satisfying the spin su(2) algebra. This operational procedure offers a concrete way of testing the relativistic features of the spin, and opens up the possibility of devising quantum information protocols for spin in the special-relativistic regime.

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  • Received 28 November 2018

DOI:https://doi.org/10.1103/PhysRevLett.123.090404

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsQuantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Flaminia Giacomini1,2, Esteban Castro-Ruiz1,2, and Časlav Brukner1,2

  • 1Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
  • 2Institute of Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria

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Issue

Vol. 123, Iss. 9 — 30 August 2019

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