### A Bayesian view of Single-Qubit Clocks, and an Energy versus Accuracy tradeoff

**2016-02-01**

1602.00508 | cond-mat.stat-mech

We bring a Bayesian approach to the analysis of clocks. Using exponential
distributions as priors for clocks, we analyze how well one can keep time with
a single qubit freely precessing under a magnetic field. We find that, at least
with a single qubit, quantum mechanics does not allow exact timekeeping, in
contrast to classical mechanics which does. We find the design of the
single-qubit clock that leads to maximum accuracy. Further, we find an energy
versus accuracy tradeoff --- the energy cost is at least $k_BT$ times the
improvement in accuracy as measured by the entropy reduction in going from the
prior distribution to the posterior distribution. We propose a physical
realization of the single qubit clock using charge transport across a
capacitively-coupled quantum dot.

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