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Video abstract for the article 'The density matrix recursion method: genuine multisite entanglement distinguishes odd from even quantum spin ladder states' by Himadri Shekhar Dhar, Aditi Sen(De) and Ujjwal Sen (Himadri Shekhar Dhar et al 2013 New J. Phys. 15 013043). Read the full article in New Journal of Physics at http://iopscience.iop.org/1367-2630/15/1/013043/article. GENERAL SCIENTIFIC SUMMARY Introduction and background. A configuration of quantum spin-1/2 particles arranged in the form of a ladder is an important system in many body physics. Spin-ladder states are potentially associated with high-temperature superconductors and quantum computers. Interestingly, such spin-ladder states are now being implemented in the laboratories in several physical systems, including atoms in optical lattices and interacting photons. However, exact calculation of the physical properties of the quantum spin-ladders is difficult as for typical states on such lattices, the number of terms in the superposition scales exponentially with the increase in system size. Main results. We introduce a technique, which we call the density matrix recursion method (DMRM) that is an efficient exact method to calculate bipartite and multipartite physical properties of large spin-ladders, in the case when the state is a superposition of lattice coverings of singlets. The method works by using a recursion of states and parameters that generates larger ladder states out of smaller ones. To demonstrate the efficiency of the method, we calculate the genuine multipartite entanglement content in such systems. We find that the well-known and intriguing disparity between even- and odd-legged ladders show up very distinctly in the behavior of genuine multiparty entanglement with increasing system size. We quantify the genuine multisite entanglement by using the generalized geometric measure. Wider implications. The DMRM is an efficient exact method to calculate physical properties in quantum spin-ladders. The formalism can be extended to study properties of quantum states of other spin lattices, and may prove useful in studying their potentiality for quantum computation.