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arXiv · 2609.07260

A Family of Completely PPT Maps

Kennett L. Dela Rosa·Iana Angela C. Fajardo·Cedie B. Reyes
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Abstract

Given $\alpha\in \mathbb R$ and $ B_1,\ldots,B_q\in M_{m,n}$, consider the map \[\Phi^{\pm}_{\alpha,\mathfrak{B}}(X)=\alpha \mbox{tr}(X) I_m\pm \sum_{s=1}^qB_sXB_s^*\ \mbox{for all}\ X\in M_n.\] In this study, necessary and sufficient conditions on $\alpha $ and $B_1,\ldots,B_q$ are given that guarantee $\Phi_{\alpha,\mathfrak{B}}^\pm$ is $k$-positive, $k$-copositive, and $k$-PPT, respectively. As application, known results about the map $\alpha \mbox{tr}(X)I_n\pm X$ are recovered. Furthermore, singular value inequalities associated with these positivity constraints are considered.

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Kennett L. Dela Rosa, Iana Angela C. Fajardo, Cedie B. Reyes. 2026-09-07. A Family of Completely PPT Maps. https://arxiv.org/abs/2609.07260

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