Symbol to represent "On the unit sphere" to laymen

Question

I am preparing a deck of slides related to quantum computing for network-administrator and business type people which involves the following diagram:

In the text I had $|\Psi> \in \{0,1\}$. I imagine this is fine for a non-mathematical audience, but it makes me uneasy since $\{0,1\}$ is the discrete set of 2 elements, so it's, like, wrong.

What's a better notation to use?

I thought of $|\Psi> \in [0,1]^3$, which is closer, but still not quite right since $|\Psi>$ is restricted to the unit sphere.

Remember, given my audience, simplicity is better than correctness.

What point(s) do you need to make that require this information as background? — John, Mar 17 '16 at 18:37
I would note first that your drawing is a sphere, not a circle. Plus, since $\Psi$ is a vector in an infinite-dimensional Hilbert space, given your audience I would simply skip this part. — Alex M., Mar 17 '16 at 18:41
@John not much, it's mainly to build intuition on qubits before we talk about Shor's algorithm and factoring (again, in an informal way) — Mike Ounsworth, Mar 17 '16 at 18:41
I use the symbol $\hat\Psi$ to represent a vector with norm $1$. — Henricus V., Mar 17 '16 at 19:33

score 1 · Answer 1 · answered Mar 17 '16 at 18:47

"Picture an exercise ball with a radius of one foot. Using extra-strength quantum super-glue we've fastened the tail of a 1-foot-long arrow to the center of the exercise ball, so it's free to pivot in any direction, and the point of the arrow touches the surface of the exercise ball."

"So $\left|1\right>$ happens when the orientation is straight up, and $\left|0\right>$ happens when the orientation is straight down."

Symbol to represent "On the unit sphere" to laymen

1 Answers1