2026/07/31 by Maxim V. Churilov
Physics and Astronomy · Mathematics · #quant-ph #math-ph #math.MP
10 pages, 3 figures. Ancillary verification code included
arxiv created 2026/08/05 · arxiv updated 2026/08/06
A Lorentz boost acts on the canonical spin of a massive particle through a momentum-dependent Wigner rotation. We show that, for one fixed observer boost, reducing over an uncertain momentum can strictly contract every pairwise spin-state trace distance without producing a channel that is degradable from the less contracted one. For spin 1/2, we first characterize the exact inversion-symmetric channel cone generated by a fixed Wigner angle and transverse momentum directions. Inside this cone lies the Pauli family Mα=diag(1-α,1-α,1-2α), 0≤α<1/2. For 0<α<β<1/2, all trace distances between distinct spin states are strictly smaller after Mβ than after Mα, yet the unique linear post-processing factor has a negative normalized Choi eigenvalue. We solve the optimization over all physical converters exactly: (1)/(2)infΛ\inCPTP‖Φβ-Λ∘Φα‖_\diamond=(α(β-α))/(2-3α), whereas the reverse deficiency is β-α. Thus the identity dominates the family, while all positive-noise members are pairwise incomparable under CPTP post-processing. The ideal construction is realized as the narrow-packet limit of pure, normalizable five-component momentum states, and explicit perturbation and finite-shot tomography bounds certify an open set of examples. Separately, every nonidentity member fails embedding in a time-homogeneous Pauli-diagonal Lindblad semigroup. Hence ordering all unassisted spin distinguishabilities does not determine the quantum statistical post-processing order.