  Phenomena induced by the existence of entanglement, such as nonlocal
correlations, exhibit characteristic properties of quantum mechanics
distinguishing from classical theories. When entanglement is accompanied by
classical communication, it enhances the power of quantum operations jointly
performed by two spatially separated parties. Such a power has been analyzed by
the gap between the performances of joint quantum operations implementable by
local operations at each party connected by classical communication with and
without the assistance of entanglement. In this work, we present a new
formulation for joint quantum operations connected by classical communication
beyond special relativistic causal order but without entanglement and still
within quantum mechanics. Using the formulation, we show that entanglement
assisting classical communication necessary for implementing a class of joint
quantum operations called separable maps can be interpreted to simulate
"classical communication" not respecting causal order. Our results reveal a new
counter-intuitive aspect of entanglement related to spacetime.
