# Local-hidden-state models for T-states using finite shared randomness

## TL;DR

This paper constructs explicit local-hidden-state models for T-states in quantum systems, demonstrating how shared randomness varies with entanglement and separability, and relating these models to Werner states.

## Contribution

It provides explicit constructions of local-hidden-state models for T-states, linking shared randomness to entanglement and separability, and relates these models to Werner states.

## Key findings

- Shared randomness decreases with increasing entanglement.
- Separable T-states can be modeled with 2 classical bits of shared randomness.
- Models reveal the separable boundary of T-states from Werner states.

## Abstract

The study of local models using finite shared randomness originates from the consideration about the cost of classically simulating entanglement in composite quantum systems. We construct explicitly two families of local-hidden-state (LHS) models for T-states, by mapping the problem to the Werner state. The continuous decreasing of shared randomness along with entanglement, as the anisotropy increases, can be observed in the one from the most economical model for the Werner state. The construction of the one for separable states shows that the separable boundary of T-states can be generated from the one of the Werner state, and the cost is 2 classical bits.