  In this paper, we introduce a new quantity called SVD entanglement entropy.
This is a generalization of entanglement entropy in that it depends on two
different states, as in pre- and post-selection processes. This SVD
entanglement entropy takes non-negative real values and is bounded by the
logarithm of the Hilbert space dimensions. The SVD entanglement entropy can be
interpreted as the average number of Bell pairs distillable from intermediates
states. We observe that the SVD entanglement entropy gets enhanced when the two
states are in the different quantum phases in an explicit example of the
transverse-field Ising model. Moreover, we calculate the R\'enyi SVD entropy in
various field theories and examine holographic calculations using the AdS/CFT
correspondence.
