Derivation of Standard Quantum Theory via State Discrimination

TL;DR

This paper characterizes standard quantum theory within general probabilistic theories by establishing a bound on state discrimination performance, providing a new operational criterion to distinguish quantum from other models.

Contribution

It introduces an equivalent condition based on state discrimination performance to uniquely identify standard quantum theory among GPTs.

Findings

Derived a condition for outperforming minimum discrimination error probability.

Characterized quantum theory by the bound on state discrimination performance.

Provided a new operational criterion to distinguish quantum from other GPTs.

Abstract

It is a key issue to characterize the model of standard quantum theory out of general models by an operational condition. The framework of General Probabilistic Theories (GPTs) is a new information theoretical approach to single out standard quantum theory. It is known that traditional properties, for example, Bell-CHSH inequality are not sufficient to single out standard quantum theory among possible models in GPTs. As a more precise property, we focus on the bound of the performance for an information task called state discrimination in general models. We give an equivalent condition for outperforming the minimum discrimination error probability under the standard quantum theory, which is given by the trace norm. Besides, by applying the equivalent condition, we characterize standard quantum theory out of general models in GPTs by the bound of the performance for state discrimination.