# The Diversity of Entanglement Structures with Self-Duality and Non-Orthogonal State Discrimination in General Probabilistic Theories

## TL;DR

This paper explores the diversity of entanglement structures within general probabilistic theories, focusing on state discrimination, symmetry, and self-duality, revealing multiple self-dual structures beyond the standard entanglement structure.

## Contribution

It introduces conditions for superior measurement performance in entanglement structures and derives the standard structure from symmetry, highlighting the existence of infinitely many self-dual structures.

## Key findings

- Equivalent conditions for measurement performance surpassing quantum theory
- Derivation of standard entanglement structure from symmetry
- Existence of infinitely many self-dual entanglement structures

## Abstract

This thesis deals with General Probabilistic Theories (GPTs) and Entanglement Structures (ESs). An ES is a possible structure of a quantum composite system in GPTs, which is not uniquely determined as the Standard Entanglement Structure (SES). It is an important problem to find reasonable postulates that determine various ESs as the SES. In order to solve this problem, this thesis explores the diversity of ESs. The topics of this thesis are roughly divided into two parts. First, this thesis considers state discrimination in ESs. As a main result, this thesis gives equivalent conditions for a given measurement in ESs to have a performance superior to standard quantum theory. Second, this thesis focuses on symmetry and self-duality. As a main result, this thesis gives derivations of the SES by symmetric conditions. On the other hand, this thesis clarifies that there are infinitely many self-dual ESs, even if they cannot be distinguished from the SES by a certain physical experiment with small errors.