Year: 2026
Type: preprint
Abstract: Quantum trajectories capture measurement-conditioned statistics beyond ensemble averages. For finite-dimensional Kraus dynamics, complete-reset and overlap conditions yield a unique invariant law with explicit geometric total-variation contraction. Under finite-reference mixing and quantitative transverse contraction, $C^2$ Kraus perturbations yield two complementary stationary limits: an affine tangent law for local fluctuations and an occupation measure for rare excursions. These limits give leading observable-response formulas, including an excursion contribution at quadratic order; both limits and coefficients depend only on reference Kraus operators and their first derivatives. For Clifford-driven monitored trajectories, group structure verifies the general hypotheses and yields geometric Wasserstein mixing uniformly over intermediate unitaries at fixed dimensions, an equivalence between uniform total-variation ergodicity and a finite nonzero rank-one Kraus product for each fixed unitary, and exact stationary tangent energies. Under partial measurement, tangent dynamics have almost surely finite memory with a sharp exponential tail; every $C^2$ state observable has vanishing first-order stationary response. For weak Hamiltonian perturbations, odd-prime Gross--Wigner mana responds linearly in the perturbation strength $θ$, whereas prime-dimensional stabilizer Rényi entropies scale as $θ^{2α}$, $θ^2\ln(1/θ)$, and $θ^2$ for fixed $0<α<1$, $α=1$, and $1<α<\infty$, respectively. Under partial measurement, the leading coefficients are strictly positive precisely for Hamiltonians outside the real span of the measurement projectors; on this quotient, the mana coefficient defines a norm and the order-one logarithmic coefficient an explicit positive-definite quadratic form.
Source: arXiv (Cornell University)
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G8238644607, G8274973648
OpenAlex ID: W7164555874