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We describe a direct method to determine the negativity of an arbitrarytwo-qubit state in experiments. The method is derived by analyzing the relationbetween the purity, negativity, and a universal entanglement witness fortwo-qubit entanglement. We show how the negativity of a two-qubit state can becalculated from just three experimentally accessible moments of the partiallytransposed density matrix of a two-photon state. Moreover, we show that thenegativity can be given as a function of only six invariants, which are linearcombinations of nine invariants from the complete set of 21 fundamental andindependent two-qubit invariants. We analyze the relation between these momentsand the concurrence for some classes of two-qubit states (including the Xstates, as well as pure states affected by the amplitude-damping andphase-damping channels). We also discuss the possibility of using the universalentanglement witness as an entanglement measure for various classes oftwo-qubit states. Moreover, we analyze how noise affects the estimation ofentanglement via this witness.

Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix