Constraint relation between steerability and concurrence for two-qubit states

TL;DR

This paper explores the relationship between steerability and concurrence in two-qubit states, establishing boundaries and criteria for detecting quantum steering using theoretical and numerical methods.

Contribution

It introduces new bounds and a sufficient criterion for quantum steering based on concurrence and purity, enhancing understanding of quantum correlations.

Findings

Derived upper and lower boundaries of steerability.

Proposed a sufficient steering criterion involving concurrence and purity.

Validated results through theoretical and numerical analysis.

Abstract

Entanglement and steering are used to describe quantum inseparabilities. Steerable states form a strict subset of entangled states. A natural question arises concerning how much territory steerability occupies entanglement for a general two-qubit entangled state. In this work, we investigate the constraint relation between steerability and concurrence by using two kinds of evolutionary states and randomly generated two-qubit states. By combining the theoretical and numerical proofs, we obtain the upper and lower boundaries of steerability. And the lower boundary can be used as a sufficient criterion for steering detection. Futhermore, we consider a special kind of mixed state transformed by performing an arbitrary unitary operation on Werner-like state, and propose a sufficient steering criterion described by concurrence and purity.