I'm having trouble accepting, intuitively, that $-\rvert1\rangle \otimes \rvert1\rangle = -\rvert11\rangle = \rvert1\rangle \otimes -\rvert1\rangle$.
It's my understanding that $ -\rvert1\rangle$ is just $\rvert1\rangle $ but time or space delayed in phase, where what "phase" means here depends on the hardware realization.
But $-\rvert1\rangle \otimes \rvert1\rangle = -\rvert11\rangle $ suggests that, if I take 2 independent systems, with the first completely out-of-phase relative to the second because (by, e.g., a Z gate), and I look at these two systems together, the composite system is completely out of phase with $\rvert11\rangle $ Somehow, I delayed one qubit, looked at it together with others, and suddenly all N of them are delayed.
All the more, if I have $\rvert111\rangle$, phase delay the first qubit with a Z gate, I get $-\rvert1\rangle \otimes \rvert11\rangle$, but now I can reassign this phase delay to any qubit and say I have $\rvert11\rangle \otimes -\rvert1\rangle$ . I.e., it's like saying qubits A-B are in phase together and collectively out of phase with qubit C, but that's the same as qubits B-C are in-phase and collectively out of phase with qubit A. This is a transitivity-violation contradiction of what we expect from equality!
My picture of phase is electrons precessing, or some other periodic process where physical objects corresponding to qubits are time delayed with definite time to each other. In this picture, phase can't be reassigned as will in the seeming contradiction I mentioned above. Is this picture incorrect?