# Perfect Discrimination of Non-Orthogonal Separable Pure States on Bipartite System in General Probabilistic Theory

## TL;DR

This paper investigates perfect discrimination of two separable pure states within a general probabilistic framework, revealing conditions for perfect distinguishability and showing some non-orthogonal states can be perfectly identified.

## Contribution

It provides a necessary and sufficient condition for perfect discrimination of separable pure states in a generalized measurement framework, including explicit measurement constructions.

## Key findings

- Some non-orthogonal separable states are perfectly distinguishable.
- The framework does not increase the maximum number of states that can be perfectly distinguished.
- Explicit measurements for perfect discrimination are derived.

## Abstract

We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The framework composed of the class of separable states and the above extended class of measurements is a typical example of general probabilistic theories. In this framework, we give a necessary and sufficient condition to discriminate two separable pure states perfectly. In particular, we derive measurements explicitly to discriminate two separable pure states perfectly, and find that some non-orthogonal states are perfectly distinguishable. However, the above framework does not improve the capacity, namely, the maximum number of states that are simultaneously and perfectly distinguishable.