Does there exist a numerical measure of entanglement? For example, if you consider two qubits, they can be in a product state (with no entanglement) like $\frac1{\sqrt2}(\lvert\uparrow\uparrow⟩+\lvert\uparrow\downarrow⟩)$, or in a Bell state (with maximum entanglement) like $\frac1{\sqrt2}(\lvert\uparrow\uparrow⟩-\lvert\downarrow\downarrow⟩)$, or somewhere in between like $\frac1{\sqrt2}[\frac1{\sqrt2}(\lvert\downarrow\uparrow⟩+\lvert\uparrow\downarrow⟩)]+\frac{i}{\sqrt2}\lvert\uparrow\uparrow⟩$.
Now it would seem logical to assign the following values of entanglement to these states: 0%, 100%, 50%.
Example of another system (more complicated) can be two harmonic oscillators, I think that they also can be entangled. For example, this state written in enery eigenvectors basis: $\frac1{\sqrt2}( |2⟩|7⟩-|4⟩|3⟩)$, appears to have maximum entanglement of 100%.
So in general I would like to know, if there exists a function (or maybe a general algorithm) $f(|\psi⟩)$ that would take a quantum state as an argument and give these values as a result?
