“…The ability to quantify, detect and analyze the structure of quantum entanglement [1] is essential for quantum computation [2][3][4], communication [5][6][7], quantum networks [8] and quantum metrology [9,10]. Moreover, an improper "amount" of entanglement, specific structure or pattern of multipartite entangled state, or action of quantum noise could severely affect the overall efficiency of quantum computation tasks [11] or performance of a given quantum protocol, such as that of entanglement purification [12].…”