QLunch: Tommaso Aschieri

Speaker: Tommaso Aschieri from QMATH

Title: Semiclassical analysis of SU(2)-equivariant quantum channels

Abstract: 

Equivariant (or covariant) channels are completely positive trace preserving maps that intertwine the action of a group G on two (irreducible) representations V and W. An interesting question to pose is to characterise the set of states that minimise the output von Neumann entropy of such channels. In the setting of SU(2), this question was partially answered by Lieb and Solovej in 2014: for a certain class of SU(2) equivariant channels, coherent states are minimisers of all concave functions of the output of channels. 

In this talk, I will present some asymptotic properties of SU(2)-equivariant quantum channels. I will show that, in the limit of large output dimension, it is possible to approximate any channel by the quantisation of a specific function on the unit sphere, related to the classical Husimi function. Using that, I will give an asymptotic expansion of the output entropy of SU(2)-equivariant quantum channels, which can be used to relate the problem of minimisation of the von Neumann entropy and the classical problem of minimisation of the Wehrl entropy.

This is joint work with B. Ruba and J. P. Solovej.