  Pseudo entropy is an interesting quantity with a simple gravity dual, which
generalizes entanglement entropy such that it depends on both an initial and a
final state. Here we reveal the basic properties of pseudo entropy in quantum
field theories by numerically calculating this quantity for a set of
two-dimensional free scalar field theories and the Ising spin chain. We extend
the Gaussian method for pseudo entropy in free scalar theories with two
parameters: mass $m$ and dynamical exponent $z$. This computation finds two
novel properties of Pseudo entropy which we conjecture to be universal in field
theories, in addition to an area law behavior. One is a saturation behavior and
the other one is non-positivity of the difference between pseudo entropy and
averaged entanglement entropy. Moreover, our numerical results for the Ising
chain imply that pseudo entropy can play a role as a new quantum order
parameter which detects whether two states are in the same quantum phase or
not.
