  We propose a general experimental scheme based on binary trees of partially
polarizing beam splitters (PPBSs) for realizing sequential unsharp measurements
of photon polarization. The sharpnesses and the bases of the particular photon
polarization measurements can be chosen arbitrarily by using corresponding
PPBSs and phase plates in the setup. In the limit of low sharpnesses the scheme
can realize sequential weak measurements, too. We develop a general formalism
for describing sequential unsharp measurements of photon polarization in which
the particular unsharp measurements are characterized by appropriate
measurement operators. We show that a straightforward experimental realization
of this model is the proposed scheme. In this formalism the output polarization
states after the sequential measurement and any correlation functions
characterizing the measurement results can be easily calculated. Our model can
be used for analyzing the consequences of applying postselection and
reselection in the measurement. We derive the anomalous mean value for an
unsharp polarization measurement with postselection and the anomalous
second-order correlation function for the sequential unsharp measurement of
photon polarization with reselection. We show that these anomalies can be
easily measured using the proposed scheme.
