aiqbench analysis
This research investigates the mathematical properties of Wigner rotations induced by Lorentz boosts on massive particle spins, demonstrating strict trace-distance contraction without resulting in degradable quantum channels. By solving for optimal converters between specific Pauli noise families, the study reveals that these boosted states are pairwise incomparable under CPTP post-processing, challenging standard assumptions about ordering spin distinguishabilities. The findings provide rigorous bounds and verification code relevant to foundational quantum information theory involving relativistic effects on qubit dynamics.
Fixed-Boost Wigner Noise: Strict Trace-Distance Contraction without Quantum Degradability
arXiv:2607.12994v2 Announce Type: replace Abstract: 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 $M_\alpha=\operatorname{diag}(1-\alpha,1-\alpha,1-2\alpha)$, $0\leq\alpha<1/2$. For $0<\alpha<\beta<1/2$, all trace distances between distinct spin states are strictly smaller after $M_\beta$ than after $M_\alpha$, yet the unique linear post-processing factor has a negative normalized Choi eigenvalue. We solve the optimization over all physical converters exactly: $\frac{1}{2}\inf_{\Lambda\in\mathrm{CPTP}}\|\Phi_\beta-\Lambda\circ\Phi_\alpha\|_\diamond=\frac{\alpha(\beta-\alpha)}{2-3\alpha}$, whereas the reverse deficiency is $\beta-\alpha$. 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.
Abstract: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 $M_\alpha=\operatorname{diag}(1-\alpha,1-\alpha,1-2\alpha)$, $0\leq\alpha<1/2$. For $0<\alpha<\beta<1/2$, all trace distances between distinct spin states are strictly smaller after $M_\beta$ than after $M_\alpha$, yet the unique linear post-processing factor has a negative normalized Choi eigenvalue. We solve the optimization over all physical converters exactly: $\frac{1}{2}\inf_{\Lambda\in\mathrm{CPTP}}\|\Phi_\beta-\Lambda\circ\Phi_\alpha\|_\diamond=\frac{\alpha(\beta-\alpha)}{2-3\alpha}$, whereas the reverse deficiency is $\beta-\alpha$. 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.
10 pages, 3 figures. Ancillary verification code included
arXiv:2607.12994 [quant-ph]
(or arXiv:2607.12994v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.12994 Focus to learn more arXiv-issued DOI via DataCite
requirements.txt
verify_fixed_boost_wigner.py
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Full text under the publisher's open licence · 294 words
