Degradation of a quantum directional reference frame as a random walk

Abstract

We investigate if the degradation of a quantum directional reference frame through repeated use can be modeled as a classical direction undergoing a random walk on a sphere. We demonstrate that the behaviour of the fidelity for a degrading quantum directional reference frame, defined as the average probability of correctly determining the orientation of a test system, can be fit precisely using such a model. Physically, the mechanism for the random walk is the uncontrollable back-action on the reference frame due to its use in a measurement of the direction of another system. However, we find that the magnitude of the step size of this random walk is not given by our classical model and must be determined from the full quantum description.

5 pages, no figures. Comments are welcome. v2: several changes to clarify the key results. v3: journal reference added, acknowledgements and references updated

References in corpus (7)

• Quantum state engineering with Josephson-junction devices
• Reference frames, superselection rules, and quantum information
• In defense of the epistemic view of quantum states: a toy theory
• Entangled quantum states as direction indicators
• Degradation of a quantum reference frame
• Optimal measurements for relative quantum information
• Operational formulation of homodyne detection

Cited by in corpus (14)

• Catalytic Coherence
• Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames
• Quantum communication using a bounded-size quantum reference frame
• Changing quantum reference frames
• Coherence and asymmetry cannot be broadcast
• A no-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting
• Generating nonclassical correlations without fully aligning measurements
• Is coherence catalytic?
• The equivalence principle and QFT: Can a particle detector tell if we live inside a hollow shell?
• Dynamics of a quantum reference frame undergoing selective measurements and coherent interactions
• Covariant catalysis requires correlations and good quantum reference frames degrade little
• Faithful extraction of quantum coherence
• Relativistic quantum information theory and quantum reference frames
• Time-reversal frameness and superselection