# What does it mean to subtract these quantum states?

For example, in particle physics the neutral pion $π^0$ exists in two quantum states $u\bar{u}$, and $d\bar{d}$; and is displayed in the form: $$\frac{u\bar{u}-d\bar{d}}{\sqrt2}$$ I understand that dividing by $\sqrt2$ means each state has 1 in 2 chance of being collapsed into. All though, why is the first state subtracting the other?

• Subtraction in a vector space is (by definition) addition of the additive inverse. In other words, $x-y$ is (by definition) $x+(-y)$. – WillO Apr 13 '17 at 4:31

Yes if you just know those probabilities, you can't tell if it is a + or - or even another phase $e^{i \phi}$. You need more information from some interference.