On the partial transpose of a Haar unitary matrix
Volume 266 / 2022
Studia Mathematica 266 (2022), 337-359
MSC: Primary 46L54; Secondary 60B20.
DOI: 10.4064/sm210517-13-12
Published online: 6 June 2022
Abstract
We consider the effect of a partial transpose on the limit $*$-distribution of a Haar distributed random unitary matrix. If we fix the number of blocks, $b$, we show that the partial transpose can be decomposed along diagonals into a sum of $b$ matrices which are asymptotically free and identically distributed. We then consider the joint effect of different block decompositions and show that under some mild assumptions we also get asymptotic freeness.
