  We study state-dependent quantum cloning which can outperform universal
cloning. This is possible by using some a priori information on a given quantum
state to be cloned. Specifically, we propose a generalization and optical
implementation of quantum optimal mirror phase-covariant cloning, which refers
to optimal cloning of sets of qubits of known modulus of expectation value of
Pauli's Z operator. Our results can be applied for cloning of an arbitrary
mirror-symmetric distribution of qubits on Bloch sphere including in special
cases the universal cloning and phase-covariant cloning. We show that the
cloning is optimal by adapting our former optimality proof for axisymmetric
cloning [Phys. Rev. 82, 042330 (2010)]. Moreover, we propose an optical
realization of the optimal mirror phase-covariant 1 to 2 cloning of a qubit,
for which the mean probability of successful cloning varies from 1/6 to 1/3
depending on prior information on the set of qubits to be cloned. The qubits
are represented by polarization states of photons generated by the type-I
spontaneous parametric down-conversion. The scheme is based on the interference
of two photons on an unbalanced polarization-dependent beam splitter with
different splitting ratios for vertical and horizontal polarization components
and the additional application of feedforward by means of Pockels cells. The
experimental feasibility of the proposed setup is carefully studied including
various kinds of imperfections and losses including: (i) finite efficiency of
generating a pair of entangled photons in the type-I spontaneous parametric
down conversion, (ii) the influence of choosing various splitting ratios of the
unbalanced beam splitter, (iii) the application of conventional and
single-photon discriminating detectors, (iv) dark counts and finite efficiency
of the detectors.
