# L\"uders Channels and the Existence of Symmetric Informationally Complete Measurements

## TL;DR

This paper links the existence of symmetric informationally complete measurements (SICs) in quantum mechanics to a specific depolarizing channel derived from L"uders channels, providing new conditions and optimality criteria.

## Contribution

It establishes an if-and-only-if condition for SIC existence based on a depolarizing channel and shows this channel meets entropic optimality criteria.

## Key findings

- Provides a necessary and sufficient condition for SIC existence.
- Identifies a depolarizing channel associated with SICs.
- Demonstrates entropic optimality of the channel.

## Abstract

The L\"uders rule provides a way to define a quantum channel given a quantum measurement. Using this construction, we establish an if-and-only-if condition for the existence of a $d$-dimensional Symmetric Informationally Complete quantum measurement (a SIC) in terms of a particular depolarizing channel. Moreover, the channel in question satisfies two entropic optimality criteria.