Constructing and Measuring in an Arbitrary 3-qubit basis

As part of a Quantum Theory project I have “constructed” an arbitrary 3-qubit basis:

$left|B_0right> =left|000right>$

$left|B_1right> = frac{1}{sqrt{2}}cos(x)(left|100right> + left|010right>) + sin(x)left|001right>$

and so on to $left|B_6right>$.

The states are orthogonal and form a proper basis set.

However, I would like to know if (and how) such a measurement can be performed.

I was looking at polarization of light and time-bins qubits experiments, but they only seem to look at creating those states, rather than performing a measurement in this basis.

Thank you in advance for your answers!