A complete characterization of eventually entanglement breaking unital quantum channels
Abstract
We obtain a complete characterization of eventually entanglement breaking (EEB) unital channels in terms of some simple commutation properties of their eigenvectors. Specifically, the following properties are equivalent for a unital channel: (i) it is EEB; (ii) it is eventually positive partial transpose (PPT); (iii) it is eventually mixed twisted dephasing; and (iv) its eigenvectors corresponding to non-zero eigenvalues commute with all its peripheral eigenvectors. Similar results hold for one-parameter semigroups of unital quantum channels, where continuity forces such semigroups to become primitive. We employ a matrix integral technique inspired by a result of Watrous. We also characterize the extreme points of the convex set of unital EB channels and, using this characterization and the theory of equiangular tight frames (ETFs), identify several extreme points beyond the twisted dephasing channels.
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BibTeX
@misc{bhat2026complete,
title = {{A complete characterization of eventually entanglement breaking unital quantum channels}},
author = {B. V. Rajarama Bhat and Pankaj Dey and Biswarup Saha},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24168},
eprint = {2609.24168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24168},
}
RIS
TY - UNPB
TI - A complete characterization of eventually entanglement breaking unital quantum channels
AU - B. V. Rajarama Bhat
AU - Pankaj Dey
AU - Biswarup Saha
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24168
UR - https://arxiv.org/abs/2609.24168
AB - We obtain a complete characterization of eventually entanglement breaking (EEB) unital channels in terms of some simple commutation properties of their eigenvectors. Specifically, the following properties are equivalent for a unital channel: (i) it is EEB; (ii) it is eventually positive partial transpose (PPT); (iii) it is eventually mixed twisted dephasing; and (iv) its eigenvectors corresponding to non-zero eigenvalues commute with all its peripheral eigenvectors. Similar results hold for one-parameter semigroups of unital quantum channels, where continuity forces such semigroups to become primitive. We employ a matrix integral technique inspired by a result of Watrous. We also characterize the extreme points of the convex set of unital EB channels and, using this characterization and the theory of equiangular tight frames (ETFs), identify several extreme points beyond the twisted dephasing channels.
ER -