Geometric Local Hidden State Model for Some Two-qubit States

TL;DR

This paper develops a geometric approach to construct optimal local hidden state models for certain two-qubit states, providing a new steering criterion and extending the method to higher dimensions like two-qutrit states.

Contribution

It introduces a geometric framework for optimal LHS models, offers a sufficient steering criterion for two-qubit states, and generalizes the approach to higher-dimensional bipartite systems.

Findings

Derived the optimal LHS model for some two-qubit states.

Established a sufficient steering criterion for all two-qubit states.

Calculated the steering bound for two-qutrit isotropic states.

Abstract

Adopting the geometric description of steering assemblages and local hidden states (LHS) model, we construct the optimal LHS model for some two-qubit states under continuous projective measurements, and obtain a sufficient steering criterion for all two-qubit states. Using the criterion, we show more two-qubit states that are asymmetric in steering scenario under projective measurements. Then we generalize the geometric description into higher dimensional bipartite cases, calculate the steering bound of two-qutrit isotropic states and make discussion on more general cases.