Einstein-Podolsky-Rosen Steerability Criterion for Two-Qubit Density Matrices

TL;DR

This paper introduces a new eigenvalue-based criterion for detecting EPR steering in two-qubit states, demonstrating its effectiveness across various state types and comparing it with existing steering inequality violations.

Contribution

It proposes a novel eigenvalue criterion for EPR steerability detection in two-qubit states, expanding the tools available for quantum correlation analysis.

Findings

Criterion effectively detects steerability in typical two-qubit states.

It predicts steerability accurately compared to existing inequalities.

Identifies a mixed state with guaranteed steerability.

Abstract

We propose a sufficient criterion ${S}=\lambda_1+\lambda_2-(\lambda_1-\lambda_2)^2<0$ to detect Einstein-Podolsky-Rosen steering for arbitrary two-qubit density matrix $\rho_{AB}$. Here $\lambda_1,\lambda_2$ are respectively the minimal and the second minimal eigenvalues of $\rho^{T_B}_{AB}$, which is the partial transpose of $\rho_{AB}$. By investigating several typical two-qubit states such as the isotropic state, Bell-diagonal state, maximally entangled mixed state, etc., we show this criterion works efficiently and can make reasonable predictions for steerability. We also present a mixed state of which steerability always exists, and compare the result with the violation of steering inequalities.