Optimizing positive maps in the matrix algebra $M_n$

Anindita Bera; Gniewomir Sarbicki; Dariusz Chruściński

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arXiv · 2309.09621

Optimizing positive maps in the matrix algebra $M_n$

Anindita Bera·Gniewomir Sarbicki·Dariusz Chruściński

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Abstract

We present an optimization procedure for a seminal class of positive maps $\tau_{n,k}$ in the algebra of $n \times n$ complex matrices introduced and studied by Tanahasi and Tomiyama, Ando, Nakamura and Osaka. Recently, these maps were proved to be optimal whenever the greatest common divisor $GCD(n,k)=1$. We attain a general conjecture how to optimize a map $\tau_{n,k}$ when $GCD(n,k)=2$ or 3. For $GCD(n,k)=2$, a series of analytical results are derived and for $GCD(n,k)=3$, we provide a suitable numerical analysis.

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BibTeX RIS

Anindita Bera, Gniewomir Sarbicki, Dariusz Chruściński. 2023-09-18. Optimizing positive maps in the matrix algebra $M_n$. https://arxiv.org/abs/2309.09621

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