bibkey: mukherjeeganguly2025network
authors: Kaushiki Mukherjee; Nirman Ganguly
year: 2025
title: "Network nonlocality breaking channels"
doi: null
url: https://arxiv.org/abs/2510.26417v1
claim: "The paper studies channels that destroy the violation of n-local inequalities in linear quantum networks, gives sufficient conditions on the parameters of a class of non-unital qubit channels under which k uses of the channel destroy the non n-local resource of linear n-local networks (Theorem 3), and conjectures from numerical comparison with the channel conditions that every non-unital channel of the class is non n-locality breaking (Conjecture 1)."
strata_touched:
  - D5/S3/Quantum/QuantumChannels/NonUnitalNetworkConditionImplication
license: citation-only
triage: anchor

Network nonlocality breaking channels

K. Mukherjee and N. Ganguly, arXiv:2510.26417v1 (2025). Quotations are from the v1 TeX source.

The conditions on the parameters of the non-unital channel class, Eq. (nu3):

$|{\lambda }_1|\le 1$, $|{\lambda }_3|+|t|\le 1$, ${\lambda }_1^2+t^2\le (1-|{\lambda }_3|{)}^2$

Theorem 3 and its sufficient condition, Eq. (resnon1):

If any non unital channel ${\mathcal{N}}_{NU}$ from the class specified by Eqs.(nu1, nu2) be such that channel parameters satisfy $(|t|+|{\lambda }_3|{)}^2+{\lambda }_1^2\le 1$ and $2t^2\cdot {\lambda }_1^2+{\lambda }_1^4+(|t|+|{\lambda }_3|{)}^4\le 1$ then ${\mathcal{N}}_{NU}$ is $k$-use non $n$-locality breaking channel up to $n$-local inequality Eq.(ineqb) in any linear $n$-local network.

The observation and Conjecture 1:

Comparing Eq.(resnon1) with that of the conditions provided by Eq.(nu3) over the channel ${\mathcal{N}}_{NU},$ it is observed that there exist no region in parameter space for which Eq.(resnon1) is violated whereas Eq.(nu3) is satisfied. However, a formal proof of the same is beyond the scope of present work. We thus provide the following conjecture:

Conjecture.1: Any non-unital channel from ${\mathcal{N}}_{NU}$ (Eqs.(nu1, nu2)) acts as a non $n$-locality breaking channel in ${\mathbf{N}}_{lin}$.

Verified locator

Source: https://arxiv.org/abs/2510.26417v1

• URL: https://arxiv.org/abs/2510.26417v1 (source Network_Nonlocality.tex, md5 6bb7806236c7d6b0bcaa73d3eed0bc28):
  • the channel conditions, Eq. (nu3), l. 211–215;
  • Theorem 3 and Eq. (resnon1), l. 714–721;
  • the observation and Conjecture 1, l. 733–734.