We study an exact local compression of a quantum bipartite state; that is,
applying local quantum operations to the state to reduce the dimensions of
Hilbert spaces while perfectly maintaining the correlation. We provide a closed
formula for calculating the minimal achievable dimensions, provided as a
minimization of the Schmidt rank of a particular pure state constructed from
that state. Numerically more tractable upper and lower bounds of the rank were
also obtained. Subsequently, we consider the exact compression of quantum
channels as an application. Using this method, a post-processing step that can
reduce the output dimensions while retaining information on the output of the
original channel can be analyzed.Comment: 9 pages, 1figure, comments are welcom