General Schemes for Quantum Entanglement and Steering Detection

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.