Usually, in undergrad QM, we see states such as ________. | psi rangle_ pm= frac1 sqrt 2(|01 rangle pm|10 rangle). Where trivially the + state is symmetric, and the - state is antisymmetric. However, I am a bit confused by the particle exchange procedure. I've mostly convinced myself it is swapping the contents within each ket, rather than swapping the kets themselves. I reason this because there may be a state | phi rangle=|00 rangle, which has to be symmetric, but there are no other terms to swap it with, although I'm not confident. I ask this question because I'm wondering about the symmetry of the state frac1 sqrt 2(|00 rangle-|11 rangle). If in fact (as I think), we flip the numbers within each ket, then this state is symmetric. However if we flip the kets themselves, then this state is antisymmetric. Can someone provide insight into this with a physical interpretation?