Feasibility Ordering of Entanglement-Source Placement for Qubit Channels
Abstract
This work studies the placement of an entanglement source along a communication line formed by two noisy qubit channels. Recent work argued, on analytical and numerical grounds, that midpoint placement should be at least as favorable as endpoint placement. Here it is shown that, for arbitrary qubit channels, if a sequential composition can preserve entanglement, then the corresponding parallel action cannot annihilate all entanglement. The proof uses the transpose-factorization criterion introduced in that recent work. Quantum Sinkhorn scaling converts every strictly positive qubit channel into a unital representative, and the special normal form of unital qubit channels then yields the required factorization of the transposed map through the original channel. Depolarizing regularization and the closedness of the set of entanglement-breaking channels extend the result to arbitrary channels. Consequently, Λ1 ⊗ Λ2 ∈ EA implies Λ2 ∘ Λ1 ∈ EB, and, by exchanging the two channels, the same holds for the opposite composition order. This proves the recent conjecture that midpoint placement is optimal for all qubit channels, in the feasibility sense in which that optimality was originally defined.
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BibTeX
@misc{gonzalez2026feasibility,
title = {{Feasibility Ordering of Entanglement-Source Placement for Qubit Channels}},
author = {Samuel Marquez Gonzalez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18803},
eprint = {2609.18803},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18803},
}
RIS
TY - UNPB
TI - Feasibility Ordering of Entanglement-Source Placement for Qubit Channels
AU - Samuel Marquez Gonzalez
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18803
UR - https://arxiv.org/abs/2609.18803
AB - This work studies the placement of an entanglement source along a communication line formed by two noisy qubit channels. Recent work argued, on analytical and numerical grounds, that midpoint placement should be at least as favorable as endpoint placement. Here it is shown that, for arbitrary qubit channels, if a sequential composition can preserve entanglement, then the corresponding parallel action cannot annihilate all entanglement. The proof uses the transpose-factorization criterion introduced in that recent work. Quantum Sinkhorn scaling converts every strictly positive qubit channel into a unital representative, and the special normal form of unital qubit channels then yields the required factorization of the transposed map through the original channel. Depolarizing regularization and the closedness of the set of entanglement-breaking channels extend the result to arbitrary channels. Consequently, Λ_1 ⊗ Λ_2 ∈ EA implies Λ_2 ∘ Λ_1 ∈ EB, and, by exchanging the two channels, the same holds for the opposite composition order. This proves the recent conjecture that midpoint placement is optimal for all qubit channels, in the feasibility sense in which that optimality was originally defined.
ER -