bibkey: ziman2001quantumhomogenization authors: M. Ziman; P. Stelmachovic; V. Buzek; M. Hillery; V. Scarani; N. Gisin year: 2001 title: “Quantum homogenization” doi: null url: https://arxiv.org/abs/quant-ph/0110164v1 claim: “The partial-swap unitary and its reduced state formula supply a standard isotropic qubit interaction model.” strata_touched: [] license: citation-only triage: anchor

Partial swap and homogenization

The cited primary record is arXiv:quant-ph/0110164v1. The source defines the swap operator and the partial-swap unitary $P(\eta )=\cos (\eta )I+i\sin (\eta )\mathsf{S}$, and derives the reduced single-collision and fresh-reservoir recurrences.

The LocalClock application uses the sign identification $\eta =-gt$ and the special reservoir state $I/2$ to obtain the isotropic reduced map. Its retained-environment two-half-wait history is calculated directly from the swap involution. The cited homogenizer convention uses fresh reservoir particles, so it does not supply the retained-environment return, the five-mode phase source, or a process-tensor identification.