  In the problem of entanglement there exist two different notions. One is the
entanglement of a quantum state, characterizing the state structure. The other
is entanglement production by quantum operators, describing the action of
operators in the given Hilbert space. Entanglement production by statistical
operators, or density operators, is an important notion arising in quantum
measurements and quantum information processing. The operational meaning of the
entangling power of any operator, including statistical operators, is the
property of the operators to entangle wave functions of the Hilbert space they
are defined on. The measure of entanglement production by statistical operators
is described and illustrated by entangled quantum states, equilibrium Gibbs
states, as well as by the state of a complex multiparticle spinor system. It is
shown that this measure is in intimate relation to other notions of quantum
information theory, such as the purity of quantum states, linear entropy, or
impurity, inverse participation ratio, quadratic R\'{e}nyi entropy, the
correlation function of composite measurements, and decoherence phenomenon.
This measure can be introduced for a set of statistical operators
characterizing a system after quantum measurements. The explicit value of the
measure depends on the type of the Hilbert space partitioning. For a general
multiparticle spinor system, it is possible to accomplish the particle-particle
partitioning or spin-spatial partitioning. Conditions are defined showing when
entanglement production is maximal and when it is zero. The study on
entanglement production by statistical operators is important because,
depending on whether such an operator is entangling or not, it generates
qualitatively different probability measures, which is principal for quantum
measurements and quantum information processing.
