Tighter Einstein-Podolsky-Rosen steering inequality based on the sum uncertainty relation

TL;DR

This paper introduces a new, tighter Einstein-Podolsky-Rosen steering inequality based on the sum uncertainty relation, improving the detection of steerability in both discrete and continuous variable quantum systems.

Contribution

It derives a novel steering inequality from the sum uncertainty relation and demonstrates its effectiveness in revealing steerability in various quantum states, surpassing previous criteria.

Findings

Optimal steering range for two qubit Werner states identified.

Non-Gaussian states show greater violation of the new inequality.

The sum steering inequality is tighter than Reid and entropic criteria.

Abstract

We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion when applied to discrete variables yields the optimum steering range for two qubit Werner states in the two measurement and two outcome scenario. We further employ the derived steering relation for several classes of continuous variable systems. We show that non-Gaussian entangled states such as the photon subtracted squeezed vacuum state and the two-dimensional harmonic oscillator state furnish greater violation of the sum steering relation compared to the Reid criterion as well as the entropic steering criterion. The sum steering inequality provides a tighter steering condition to reveal the steerability of continuous variable states.