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

Abstract

We study quantum processes in which information extracted from a forward simulation is returned as 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. Four results separate notions that informal discussions of "information from the future" often conflate. A two-parameter unitary-dilation family yields a closed-form, globally attractive, coherent fixed point (Proposition 1), yet is entanglement breaking whenever future records are perfectly distinguishable (Lemma 1). Releasing that orthogonality, a four-parameter partial-swap family admits a nonempty open non-entanglement-breaking region (Proposition 2), with an explicit Choi partial-transpose neighborhood of half-width $0.0163\pi$ (Proposition 3). Combining outward-rounded interval enclosures with perturbation bounds tracking the channel and its stationary-state drift, we certify an explicit parameter square of half-width $0.0013\pi$ on which the feedback channel is simultaneously strictly contractive (margin $\ge 0.237$), coherent ($\ge 0.416$), informative about the designated future variable ($\ge 0.172$ bits), and non-entanglement-breaking (NPT margin $\ge 0.188$) (Proposition 4). Direct evaluation shows all four properties persisting over a region an order of magnitude larger, so the certified square is a proof of principle rather than a phase boundary. All enclosures and margins are confirmed by a machine-verified ball-arithmetic certificate, and the complete code and certificate accompany the paper.

11 pages, 4 figures. Ancillary files include a machine-verified interval certificate (Arb/python-flint, 256-bit ball arithmetic), an independent second-stack audit (mpmath), and all research code. Submitted to Foundations of Physics