In classical physics, a system can be described by a set of numbers whose values can all be measured using a single instance of that system. In quantum mechanics, a system is characterised by the values of observables where those values are represented by Hermitian matrices. To describe how information is transferred between quantum systems you have to describe the ways in which the observables of one system depend on those of another.
In general, an observable does not represent just a single valued measurable quantity changing over time. Rather, it represents a more complex structure that involves multiple different versions of that quantity interfering with one another. And if there are going to be multiple versions of each system, then any given system has to carry information about how a particular version of that system will interact with a particular version of another system. In general, you can't get that sort of information by measuring just one system and for that reason it is called locally inaccessible information. An explanation of how locally inaccessible information gives rise to EPR correlations, teleportation etc by entirely local interactions is given here: