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arXiv:2506.01851 · Quantum Information Processing

Bayesian and Markovian classical feedforward for discriminating qubit channels

Milajiguli Rexiti, Stefano Mancini

Published Jan 20, 2026• 0 citations
arXivHTMLPDF
DOI
10.1007/s11128-025-05042-8

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The author develops the experimental layer of the framework introduced in the foundational Preprint I. Seven families of falsifiable predictions (F1–F7) are stated and matched to ten falsification criteria (F-T1–F-T10). The predictions cover: τ-window scaling laws under monitored feedback and non-Markovian memory; a 3-qubit ontological feedforward discriminator constructed to separate synchronisation-based from entanglement-based metric emergence; a directional-asymmetry test Δ(τ) with null control; a 4-qubit triangle-inequality test on the metric-compatibility regime; an asymptotic large-deviation consistency channel as cross-cutting envelope; a coherence-affected entropy-production consistency target; and a sync-rate scaling under Dicke collective dissipation. A worked-case reanalysis of Micadei et al. (2019) under the non-Markovian channel of P1 demonstrates non-vacuity of the framework on existing experimental data within a factor ≈ 2.5 on a nine-decade timescale range. The operational definition of the memory timescale τₘₑₘ was fixed prior to numerical evaluation as a matter of pre-registration discipline, with an analytic zero-crossing alternative computed for transparency and explicitly rejected under the conservative bound. A structured Nakajima–Zwanzig–TCL2 sketch indicating the sign and structure of the next-to-leading-order correction for the Micadei interaction Hamiltonian is provided in Appendix E-II, identifying this residual as a target for next-to-leading-order refinement in the smallness parameter (Φ_NM − 1).
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A seminal result of Hastings showed that entangled inputs can increase the rate of classical communication through independent uses of a quantum channel. While Hastings' result proved the existence of this phenomenon, it has remained a major open problem to find an explicit channel with this property. In this work, we resolve this question by constructing an explicit family of finite-dimensional quantum channels for which entangling inputs between pairs of channel uses yields an unbounded separation from the achievable communication rate using unentangled inputs. We describe a circuit implementation of our channel that uses only deterministic qudit Clifford unitaries and a single binary measurement with classical feedforward. The key ingredient is a careful design of the measurement and feedforward process that yields the required one-copy and two-copy output entropy bounds from moment estimates alone, without requiring strong convergence of the underlying unitary family.