Multipartite distribution property of one way discord beyond measurement

We investigate the distribution property of one way discord in the multipartite system by introducing the concept of polygamy deficit for one way discord. The difference between one way discord and quantum discord is analogue to the one between entanglement of assistance and entanglement of formation. For tripartite pure states, two kinds of polygamy deficits are presented with the equivalent expressions and physical interpretations regardless of measurement. For four-partite pure states, we provide a condition which makes one way discord polygamy satisfied. In addition, we generalize these results to the case for NN-partite pure states. Those results can be applicable to multipartite quantum systems and are complementary to our understanding of the shareability of quantum correlations.