  In this paper, firstly considering that in separable states, the measurement
of one particle has no effect on the measurement of the second particle, we
show that Alice and Bob can find directions in which the results of their
measurements on the spin of the particle are always maximized. In other words,
the state of the particle is an eigenstate for the operator that is applied in
that direction, so the sum of the spins of two particles can have a maximum
value. We will argue that in entangled states, due to the effect of particle
measurement results on each other, Alice and Bob cannot find the desired
operators. Therefore, in such measurements, the total spin of the particles
will always be less than the mentioned maximum. But we ask them to try and
measure in directions that will get the most value. Because this value is
maximum for separable states and minimum for fully entangled states, and for
the rest of the states, it will be proportional to the degree of entanglement
between the two maximum and minimum values, we set this parameter as We are
calling it the "separability index". Then, based on this index, the measure of
entanglement was introduced and extended to states with higher dimensions. In
the end, examples of di-qubit states di-qutrit states, and di-qudit states were
investigated and the efficiency of the measure was confirmed by the results of
the examples. Considering that in this measure, the values of entanglement are
calculated based on the expectation values and we can measure the expectation
values in the experiment, we hope to be one step closer to the testability of
the entanglement value.
