# The principle of information symmetry constrains the state-space in any physical theory

## TL;DR

The paper introduces the principle of information symmetry, showing it constrains the state-space in physical theories and supports the axiomatic derivation of quantum theory.

## Contribution

It proposes the information symmetry principle and demonstrates its role in constraining state-space structures, aligning with quantum theory and excluding some alternative theories.

## Key findings

- Information symmetry constrains state-space structures.
- The principle rules out certain classes of theories.
- Quantum theory remains compatible with information symmetry.

## Abstract

Symmetry shares an entwined history with the structure of physical theory. We propose a consequence of symmetry towards the axiomatic derivation of Hilbert space quantum theory. We introduce the notion of information symmetry (IS) and show that it constraints the state-space structure in any physical theory. To this end, we study the minimal error binary state discrimination problem in the framework of generalized probabilistic theories. A theory is said to satisfy IS if the probability of incorrectly identifying each of two randomly prepared states is same for both the states. It is found that this simple principle rules out several classes of theories while being perfectly compatible with quantum theory.