  We propose new entanglement measures as the detection performance based on
the hypothesis testing setting. We clarify how our measures work for detecting
an entangled state by extending the quantum Sanov theorem. Our analysis covers
the finite-length setting. Exploiting this entanglement measure, we present how
to derive entanglement witness to detect the given entangled state by using the
geometrical structure of this measure. We derive their calculation formulas for
maximally correlated states, and propose their algorithms that work for general
entangled states. In addition, we investigate how our algorithm works for
solving the membership problem for separability.
