Population-only decay map for n-qubit n-partite inseparability detection

We introduce a new positive linear map for a single qubit. This map is a decay only in populations of a single-qubit density operator. It is shown that an n-fold product of this map may be used for a detection of n-partite inseparability of an n-qubit density operator (i.e., detection of impossibility of representing a density operator in the form of a convex combination of products of density operators of individual qubits). This product map is also investigated in relation to a variant of the entanglement detection method mentioned by Laskowski and Zukowski.