General Schemes for Quantum Entanglement and Steering Detection

TL;DR

This paper introduces a versatile method for detecting quantum entanglement and steering using arbitrary measurements, unifying existing criteria and advancing understanding of quantum uncertainty and state reconstruction.

Contribution

It presents a general detection framework applicable to entanglement and steering, introduces the concept of measurement orbit, and extends SIC-POVM to symmetric complete measurements for analytical state reconstruction.

Findings

New criteria unify existing entanglement detection methods.

Method applicable to steering detection without prior state knowledge.

Introduction of measurement orbit enhances understanding of uncertainty relations.

Abstract

Separability problem is a long-standing tough issue in quantum information theory. In this paper, we propose a general method to detect entanglement via arbitrary measurement $\boldsymbol{X}$, by which several novel criteria are established. The new criteria are found incorporate many of the prevailing ones in the literatures. Our method is applicable as well to the steering detection, which possesses a merit of ignoring the knowledge of involved quantum states. A concept of measurement orbit, which plays an important role in the detection of entanglement and steering, is introduced, which enlightens our understanding of uncertainty relation. Moreover, an extension of symmetric informationally complete positive operator-valued measures (SIC-POVM), viz. symmetric complete measurements (SCM), is proposed, and employed to reconstruct the quantum state analytically.