On the classification of two-qubit group orbits and the use of coarse-grained 'shape' as a superselection property

TL;DR

This paper explores how coarse-grained 'shape' properties can classify two-qubit states under symmetry constraints, providing a new perspective on state interconversion and quantum simulation protocols.

Contribution

It introduces a shape-based classification framework for two-qubit states respecting symmetries, offering a complete solution for the rotation group case and analyzing extensions.

Findings

Complete classification for two-qubit states under rotation symmetry

Analysis of coarse-grained 'shape' properties for state interconversion

Discussion of potential extensions to more general cases

Abstract

Recently a complete set of entropic conditions has been derived for the interconversion structure of states under quantum operations that respect a specified symmetry action, however the core structure of these conditions is still only partially understood. Here we develop a coarse-grained description with the aim of shedding light on both the structure and the complexity of this general problem. Specifically, we consider the degree to which one can associate a basic `shape' property to a quantum state or channel that captures coarse-grained data either for state interconversion or for the use of a state within a simulation protocol. We provide a complete solution for the two-qubit case under the rotation group, give analysis for the more general case and discuss possible extensions of the approach.