  Studies on symmetric extendibility of quantum states become especially
important in a context of analysis of one-way quantum measures of entanglement,
distilabillity and security of quantum protocols. In this paper we analyse
composite systems containing a symmetric extendible part with a particular
attention devoted to one-way security of such systems. Further, we introduce a
new one-way monotone based on the best symmetric approximation of quantum
state. We underpin those results with geometric observations on structures of
multi-party settings which posses in sub-spaces substantial symmetric
extendible components. Finally, we state a very important conjecture linking
symmetric-extendibility with one-way distillability and security of all quantum
states analyzing behavior of private key in neighborhood of symmetric
extendible states.
