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A dynamical map is a map which takes one density operator to another. Such amap can be written in an operator-sum representation (OSR) using a spectraldecomposition. The method of the construction applies to more general mapswhich need not be completely positive. The OSR not unique; there is a freedomto choose the set of operators in the OSR differently, yet still obtain thesame map. Here we identify all maps which are equivalent to a given map.Whereas the freedom for completely positive maps is unitary, the freedom formaps which are not necessarily completely positive is pseudo-unitary.

All maps equivalent to a given map, completely positive or not