  We theoretically and experimentally investigate conditional enhancement of
overall coherence of quantum states by probabilistic quantum operations that
apply to the input state a quantum filter diagonal in the basis of incoherent
states. We identify the optimal filters that for a given probability of
successful filtering maximize the output coherence. We verify the performance
of the studied quantum filters in a proof-of-principle experiment with linear
optics, where a pair of two-level quantum systems is represented by
polarization states of two photons. We comprehensively characterize the
implemented two-qubit linear optical quantum filters by full quantum process
tomography and we experimentally observe the optimal quantum coherence
enhancement by quantum filtering.
