[abdullahkhalids]

> (It’s important to note that a ket is not distinguishable from a vector. It’s actually called so because of a notational convention, not because it has deeper underlying meaning. However, physicists will still use the word “ket” instead of “vector” or “quantum state” even if they’re not emphasizing notation.)

This is not correct when you start talking about continuous-variable states. In the (canonical) position basis, the state of an infinite-dimensional system is commonly expressed as \ket{\psi} = \int \psi(x)\ket{x}dx. Here {\ket{x}} are a basis set, but not square-integrable, since \bra{x}\ket{x} = deltafunction(0). Hence \ket{x} is not a valid quantum mechanical state.

[reikonomusha]

Kets sometimes even represent vector-valued functions (e.g., |f(t)> = e^(iHt)|0> or so) which in and of themselves aren’t states, but representations of system dynamics. We could pontificate as to whether |f(t)> is the function or is merely the image of t -> |f(t)> at some t. :)

In any event, I’m speaking in the context of my comment and of the article: (gate-based) quantum computation. Here, 9 out of 10 dentists will use a ket to denote the (computational) state of the quantum computer. Infinite dimensional states and bases aren’t pertinent at the level of logical computation.