Degradation of a quantum reference frame

Abstract

We investigate the degradation of reference frames, treated as dynamical quantum systems, and quantify their longevity as a resource for performing tasks in quantum information processing. We adopt an operational measure of a reference frame's longevity, namely, the number of measurements that can be made against it with a certain error tolerance. We investigate two distinct types of reference frame: a reference direction, realized by a spin-j system, and a phase reference, realized by an oscillator mode with bounded energy. For both cases, we show that our measure of longevity increases quadratically with the size of the reference system and is therefore non-additive. For instance, the number of measurements that a directional reference frame consisting of N parallel spins can be put to use scales as N^2. Our results quantify the extent to which microscopic or mesoscopic reference frames may be used for repeated, high-precision measurements, without needing to be reset - a question that is important for some implementations of quantum computing. We illustrate our results using the proposed single-spin measurement scheme of magnetic resonance force microscopy.

9 pages plus appendices, 4 figures, published version

References in corpus (7)

• Classical and quantum communication without a shared reference frame
• Realistic clocks, universal decoherence and the black hole information paradox
• Decoherence-full subsystems and the cryptographic power of a private shared reference frame
• Operational formulation of homodyne detection
• Optimal measurements for relative quantum information
• Entanglement under restricted operations: Analogy to mixed-state entanglement
• Entanglement of identical particles and reference phase uncertainty

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• Time-reversal frameness and superselection