论文标题
关于Tsallis相对操作员熵的一些评论
Some remarks on Tsallis relative operator entropy
论文作者
论文摘要
本文打算对TSALLIS相对操作员熵$ {{t} _ {v}} \ left（a | b \ right）= \ frac {a {{\ natural} _ {v} _ {v}} b-a} {v} $。让$ a $ a $ b $是两个正面可逆操作员，其中包含的光谱$ j \ subset（0，\ infty）$。我们证明了任何$ v \ in \ in \ left [-1,0 \右）\ cup \ left（0,1 \右] $，$$（\ ln_v t）a+\ left（a {{\ natural} _ {v} _ {v}}}} b+ta { {{t} _ {v}} \ left（a | b \ right）\ le（\ ln_v s）a+{{s}^{v-1}} \ left（b-sa \ right）$尤其是建立的。 此外，我们介绍了指数类型的相对操作员熵，这是该视角的特殊情况，我们在它们之间以及通常的相对操作员熵中给出了不平等。
This paper intends to give some new estimates for Tsallis relative operator entropy ${{T}_{v}}\left( A|B \right)=\frac{A{{\natural}_{v}}B-A}{v}$. Let $A$ and $B$ be two positive invertible operators with the spectra contained in the interval $J \subset (0,\infty)$. We prove for any $v\in \left[ -1,0 \right)\cup \left( 0,1 \right]$, $$ (\ln_v t)A+\left( A{{\natural}_{v}}B+tA{{\natural}_{v-1}}B \right)\le {{T}_{v}}\left( A|B \right) \le (\ln_v s)A+{{s}^{v-1}}\left( B-sA \right) $$ where $s,t\in J$. Especially, the upper bound for Tsallis relative operator entropy is a non-trivial new result. Meanwhile, some related and new results are also established. In particular, the monotonicity for Tsallis relative operator entropy is improved. Furthermore, we introduce the exponential type relative operator entropies which are special cases of the perspective and we give inequalities among them and usual relative operator entropies.
