Confusability graphs for symmetric sets of quantum states

TL;DR

This paper introduces a graph-theoretic approach to analyze symmetric quantum states, revealing structural insights that aid in optimal group action estimation and identifying decoherence-free subspaces.

Contribution

It presents a novel graph-based framework for studying symmetric quantum states and applies it to quantum estimation and decoherence-free subspace identification.

Findings

Connected components reveal state orthogonality structure

Graph analysis improves group action estimation strategies

Method aids in finding decoherence-free subspaces

Abstract

For a set of quantum states generated by the action of a group, we consider the graph obtained by considering two group elements adjacent whenever the corresponding states are non-orthogonal. We analyze the structure of the connected components of the graph and show two applications to the optimal estimation of an unknown group action and to the search for decoherence free subspaces of quantum channels with symmetry.