  A topic about synthesis of quantum images is proposed, and a specific phase
rotation transform constructed is adopted to theoretically realise the
synthesis of two quantum images. The synthesis strategy of quantum images
comprises three steps, which include:
  (1) In the stage of phase extraction, we obtain the phases of the state of
the quantum image by transforming the state of the quantum image to prepare the
conditions for multiple phases extraction.
  (2) In the stage of rotation operator construction, the phases obtained in
the first stage are used to construct the rotation operator where a mechanism
is introduced into it to reduce the phase overflow.
  (3) In the stage of application of the rotation operator, we apply the
operator constructed in the second stage on the state of quantum image to get a
goal state.
  Additionally, numerical analysis gives the joint uncertainty relation of the
pixel of the synthesized quantum image.
  The analysis result about the compression ratio indicates that the phase
rotation transform and the overflow control mechanism are effective.
