  Here we focus on the measurement induced nonlocality and present a
redefinition in terms of the skew information subject to a broken observable.
It is shown that the obtained quantity possesses an obvious operational
meaning, can tackle the noncontractivity of the measurement induced nonlocality
and has analytic expressions for many quantum states. Most importantly, an
inverse approximate joint diagonalization algorithm, due to its simplicity,
high efficiency, stability, and state independence, is presented to provide
almost analytic expressions for any quantum state, which can also shed light on
other aspects in physics.
