Propagation of conditional nonclassical reservoir states during quantum decoherence

Decoherence is usually described as the loss of local quantum coherence after tracing over environmental degrees of freedom. This reduced description, however, hides the reservoir state that carries the lost coherence. Here we show that spin-boson decoherence can write a postselectable nonclassical imprint into a structured bosonic reservoir. We map zero- and finite-temperature reservoirs to one-dimensional chains, evolve the joint qubit-reservoir state with tensor-network dynamics, and reconstruct the Wigner function of a time-adaptive leading collective reservoir coordinate after transverse qubit readout. The conditioned mapped-reservoir coordinate develops Wigner negativity and interference fringes that are strongly suppressed in the unconditional reservoir state. A parameter sweep shows that the spectral exponent and temperature control the visibility of this conditional nonclassicality, the mapped-chain excitation transport, and the degree to which a single collective coordinate captures the imprint. These results provide a branch-resolved phase-space picture of decoherence: the reservoir is not only a sink for qubit coherence, but can carry a measurement-conditioned nonclassical state in a collective mapped coordinate.