Sometimes, there is an absolute limit on the number of terms an officeholder can serve, while, in other cases, the restrictions are merely on the number of consecutive terms.
For example, Maxwell's Equations would always be capitalized, while quantum mechanics is usually un-capitalized. I searched half a dozen sites for an answer to this but found no clue about a rule. So go either way that makes you happy, but (most of all) be consistent.
Quantum state. In quantum physics, quantum state refers to the state of an isolated quantum system. A quantum state provides a probability distribution for the value of each observable, i.e. for the outcome of each possible measurement on the system.