Wigner and Yanase conjectured the more general problem of the concavity of the function \(\rho \mapsto \text {Trace}\ \rho ^pK^*\rho ^{1-p}K\). Lieb gave an actual connection with something then known as the strong subadditivity of the quantum entropy conjecture, which was due to Ruelle and Robinson. Lieb proved the concavity of that function, and this deep result is known as the Lieb’s concavity theorem. In this paper, the observation that Marechal’s perspective leads to a generalization of the Lieb’s concavity theorem is presented. Indeed, we give a multivariate version of the well known Lieb’s concavity theorem and its extension.

Wigner和Yanase推测了函数\（\ rho \ mapsto \ text {Trace} \ \ rho ^ pK ^ * \ rho ^ {1-p} K \）的凹性的更笼统的问题。里布（Lieb）与后来被称为量子熵猜想的强次可加性的事物产生了实际联系，这是由于鲁伊尔（Ruelle）和罗宾逊（Robinson）所致。Lieb证明了该函数的凹性，这个深层的结果被称为Lieb凹性定理。在本文中，提出了关于Marechal的观点导致Lieb凹度定理的推广的观察。的确，我们给出了著名的利勃凹性定理及其扩展的多元版本。