Quantum Joke (not a real joke, not a riddle) Supposing I want to make a quantum joke, like writing this on a coffee machine:
$$| \text{Status}\rangle = \frac{1}{\sqrt{2}}\ \big( | \text{Working}\rangle \color{red}{\pm}  | \text{Down}\rangle \big) \, ,$$
should I choose the $\color{red}{+}$ or the $\color{red}{-}$ sign, or is it the same? Why?
 A: Perhaps you don't want a quantum superposition, but just a statistical mixture:
$$\rho = \begin{pmatrix}1/2 & 0 \\ 0 & 1/2\end{pmatrix}$$
Although I'm not 100% sure that this will describe your situation any better...
A: The signs are important for fixing an out of order machine. Define the states $|\pm\rangle$ as:
$$|\pm\rangle = \frac{1}{\sqrt{2}}\left[\left |\text{Working}\right\rangle\pm \left |\text{Down}\right\rangle\right]$$
And we define the observable $O$ as:
$$O = |+\rangle\langle + |\  - \  |-\rangle\, \langle -|$$
Suppose then that coffee machine is out of order. To fix it, you measure $O$ and then you measure if it is working, if not you repeat the procedure of measuring $O$ and then checking if it is working. At each step you have 50% probability that it will be found to be working. 
A: If you want to declare indeterminacy and a probability of being either working or down you should use the vector notation:
       (working )

Status> = 
       ( down)

Status being the column vector analogous to the column state vector of the wavefunction in a matrix representation
The user would be the operator :)
