  Although quantum entanglement has already been verified experimentally and
applied in quantum computing, quantum sensing and quantum networks, most of the
existing measures cannot characterize the entanglement faithfully. In this
work, by exploiting the Schmidt decomposition of a bipartite state
$|\psi\rangle_{AB}$, we first establish a one-to-one correspondence relation
between the characteristic polynomial of the reduced state $\rho_A$ and the
polynomials its trace. Then we introduce a family of entanglement measures
which are given by the complete eigenvalues of the reduced density matrices of
the system. Specific measures called informationally complete entanglement
measures (ICEMs) are presented to illustrate the advantages. It is demonstrated
that such ICEMs can characterize finer and distinguish better the entanglement
than existing well-known entanglement measures. They also give rise to criteria
of state transformations under local operation and classical communication.
Moreover, we show that the ICEMs can be efficiently estimated on a quantum
computer. The fully separability, entanglement and genuine multipartite
entanglement can detected faithfully on quantum devices.
