  We describe a direct method to determine the negativity of an arbitrary
two-qubit state in experiments. The method is derived by analyzing the relation
between the purity, negativity, and a universal entanglement witness for
two-qubit entanglement. We show how the negativity of a two-qubit state can be
calculated from just three experimentally accessible moments of the partially
transposed density matrix of a two-photon state. Moreover, we show that the
negativity can be given as a function of only six invariants, which are linear
combinations of nine invariants from the complete set of 21 fundamental and
independent two-qubit invariants. We analyze the relation between these moments
and the concurrence for some classes of two-qubit states (including the X
states, as well as pure states affected by the amplitude-damping and
phase-damping channels). We also discuss the possibility of using the universal
entanglement witness as an entanglement measure for various classes of
two-qubit states. Moreover, we analyze how noise affects the estimation of
entanglement via this witness.
