  We study pseudo entropy for a particular linear combination of entangled
states in qubit systems, two-dimensional free conformal field theories (CFT),
and two-dimensional holographic CFT. We observe phenomena that the pseudo
entropy can be parametrically large compared with the logarithm of the
dimension of Hilbert space. We call these phenomena pseudo entropy
amplification. The pseudo entropy amplification is analogous to the
amplification of the weak value. In particular, our result suggests the
holographic CFT does not lead the amplification as long as the non-perturbative
effects are negligible. We also give a heuristic argument when such
(non-)amplification can occur.
