Certified coherent, informative, and non-entanglement- breaking fixed points of future-referential quantum feedback

The paper studies quantum processes in which information extracted from a forward simulation is returned as an input to an earlier internal time of the simulated dynamics: externally the protocol is an ordinary causally ordered circuit, but internally it is future-referential. Contracting a process tensor with a leakage instrument and a controller induces a completely positive trace-preserving map on a message register, and we classify its fixed points by five operational properties: stability, informativeness, feedability, coherence, and preservation of quantum correlations.