# von Neumann entropy and relative position between subalgebras - Mathematics > Operator Algebras

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Abstract: We give a numerical characterization of mutual orthogonality that is,complementarity for subalgebras. In order to give such a characterization formutually orthogonal subalgebras $A$ and $B$ of the $k \times k$ matrix algebra$M k\mathbb{C}$, where $A$ and $B$ are isomorphic to some $M n\mathbb{C}$$n \leq k$, we consider a density matrix which is induced from the pair $\{A,B\}$. We show that $A$ and $B$ are mutually orthogonal if and only if the vonNeumann entropy of the density matrix is the maximum value $2\log n$, which isthe logarithm of the dimension of the subfactors.

Autor: Marie Choda

Fuente: https://arxiv.org/