  We prove an equivalence transformation between the correlation measure
functions of the causally-unbiased quantum gravity space and the
causally-biased standard space. The theory of quantum gravity fuses the dynamic
(nonfixed) causal structure of general relativity and the quantum uncertainty
of quantum mechanics. In a quantum gravity space, the events are causally
nonseparable and all time bias vanishes, which makes it no possible to use the
standard causally-biased entropy and the correlation measure functions. Since a
corrected causally-unbiased entropy function leads to an undefined, obscure
mathematical structure, in our approach the correction is made in the data
representation of the causally-unbiased space. Here we prove that the standard
causally-biased entropy function with a data correction can be used to identify
correlations in dynamic causal structures. As a corollary, all mathematical
properties of the causally-biased correlation measure functions are preserved
in the causally-unbiased space. The equivalence transformation allows us to
measure correlations in a quantum gravity space with the stable, well-defined
mathematical background and apparatus of the causally-biased functions of
quantum Shannon theory.
