Dynamics of a Quantum Reference Frame

Abstract

We analyze a quantum mechanical gyroscope which is modeled as a large spin and used as a reference against which to measure the angular momenta of spin-1/2 particles. These measurements induce a back-action on the reference which is the central focus of our study. We begin by deriving explicit expressions for the quantum channel representing the back-action. Then, we analyze the dynamics incurred by the reference when it is used to sequentially measure particles drawn from a fixed ensemble. We prove that the reference thermalizes with the measured particles and find that generically, the thermal state is reached in time which scales linearly with the size of the reference. This contrasts a recent conclusion of Bartlett et al. that this takes a quadratic amount of time when the particles are completely unpolarized. We now understand their result in terms of a simple physical principle based on symmetries and conservation laws. Finally, we initiate the study of the non-equilibrium dynamics of the reference. Here we find that a reference in a coherent state will essentially remain in one when measuring polarized particles, while rotating itself to ultimately align with the polarization of the particles.

References in corpus (4)

• Reference frames, superselection rules, and quantum information
• Degradation of a quantum reference frame
• Optimal measurements for relative quantum information
• Quantum Channels and Representation Theory

Cited by in corpus (6)

• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Quantum reference frames and deformed symmetries
• Building all Time Evolutions with Rotationally Invariant Hamiltonians
• Quantum Reference Frames and the Classification of Rotationally-Invariant Maps
• Loss of entanglement in quantum mechanics due to the use of realistic measuring rods
• A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers