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, $\Lambda_1 \otimes \Lambda_2 \in \mathrm{EA}$ implies $\Lambda_2 \circ \Lambda_1 \in \mathrm{EB}$, 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.

arXiv:2609.18803 [quant-ph]

(or arXiv:2609.18803v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.18803 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.