Infrared Quantum-Environmental Engineering Using Soft Photons as Angular-Momentum Detectors

Built upon infrared QED formulated as an open quantum system, I use the complementary soft photons as a quantum instrument. The experiment selects the hard-state code, resolved process, trajectory, accepted modes, and photon readout. QED fixes the interaction. On an eikonal-degenerate reducing code, the momentum-flow jump acts as a scalar. A Lindbladian displacement removes this common term from the dissipator. Its interference with the Low--Burnett--Kroll operator enters a finite Hamiltonian. The residual dissipator ${\cal J}_\lambda(\hat q)$ measures direction- and helicity-dependent projections of orbital and spin angular momentum. I isolate the same operator in a selective photon measurement by coherently nulling the branch-independent eikonal output. The nulled click effects and the logical dissipator scale as $E_d^2$. Both saturate at the lower infrared endpoint. In the semiclassical branch limit, the decoherence functional$$ \Gamma^{(1)}_{ab}(E_d)= \frac{e^2}{2}\sum_{\lambda=\pm}\int_0^{E_d} \frac{{\rm d}^3q}{(2\pi)^3 2\omega} \left|{\cal J}_{\lambda,a}(\hat q)-{\cal J}_{\lambda,b}(\hat q)\right|^2$$sets the soft-output overlap. Coherent prescribed currents exponentiate this functional. Repeated outputs give the exact sample complexity for hard-branch identification. General mixed outputs obey the quantum Chernoff bound. I also specialize privacy--correctability duality to the vacuum-plus-one-photon instrument. The resulting criterion identifies hard codes that hide their logical state from the retained soft output.I extend the instrument to orthogonal mode restrictions and zero-mean Gaussian soft states. I prove covariance under unitary mode transformations. I derive the equivalent positive noise-kernel form. The result promotes the finite two-path record to an operator-valued QED instrument. Soft radiation becomes a controlled probe of angular momentum.