  In an idealistic setting, quantum metrology protocols allow to sense physical
parameters with mean squared error that scales as $1/N^2$ with the number of
particles involved---substantially surpassing the $1/N$-scaling characteristic
to classical statistics. A natural question arises, whether such an impressive
enhancement persists when one takes into account the decoherence effects that
are unavoidable in any real-life implementation. In this thesis, we resolve a
major part of this issue by describing general techniques that allow to
quantify the attainable precision in metrological schemes in the presence of
uncorrelated noise. We show that the abstract geometrical structure of a
quantum channel describing the noisy evolution of a single particle dictates
then critical bounds on the ultimate quantum enhancement. Our results prove
that an infinitesimal amount of noise is enough to restrict the precision to
scale classically in the asymptotic $N$ limit, and thus constrain the maximal
improvement to a constant factor. Although for low numbers of particles the
decoherence may be ignored, for large $N$ the presence of noise heavily alters
the form of both optimal states and measurements attaining the ultimate
resolution. However, the established bounds are then typically achievable with
use of techniques natural to current experiments. In this work, we thoroughly
introduce the necessary concepts and mathematical tools lying behind
metrological tasks, including both frequentist and Bayesian estimation theory
frameworks. We provide examples of applications of the methods presented to
typical qubit noise models, yet we also discuss in detail the phase estimation
tasks in Mach-Zehnder interferometry both in the classical and quantum
setting---with particular emphasis given to photonic losses while analysing the
impact of decoherence.
