# What is the best notation to write pairs of one-qubit ket states?

I am working on coming up with practice problems for a QC course. I have a problem that considers two qubits as so:

$$|\psi_a\rangle = \alpha_a |0\rangle + \beta_a |1\rangle$$

$$|\psi_b\rangle = \alpha_b |0\rangle + \beta_b |1\rangle$$

But I found the alphas and betas combined with a's and b's very confusing. I was just wondering if there was a standard notation for this type of thing or any notation others have found easier to understand.

• The metacharacters \langle and \rangle give you the left and right angle brackets. Aug 20 '21 at 0:05
• $|\psi_a\rangle=a_0|0\rangle + a_1|1\rangle$ and $|\psi_b\rangle=b_0|0\rangle + b_1|1\rangle$? Aug 20 '21 at 13:13

I am not sure if this helps in any way but you could consider the state of an arbitrary qubit $$i$$ as:
$$|\psi_i \rangle = \alpha_i |0\rangle + \beta_i |1\rangle$$
So if $$|\psi_1 \rangle$$ and $$|\psi_2 \rangle$$ correspond to the state of qubit $$q_1$$ and $$q_2$$ then we have $$|\psi_1 \rangle = \alpha_1 |0\rangle + \beta_1 |1\rangle$$ $$|\psi_2 \rangle = \alpha_2 |0\rangle + \beta_2 |1\rangle$$
This avoids mixing $$\alpha$$, $$\beta$$ with $$a$$ and $$b$$. Again, these are just dummy variables so you can change them to whatever you want.
• Yep, this is what I would do. Sometimes I go even further and use just a single symbol $c$ for all coefficients, with an extra subscript giving the basis state. For example: $|\psi_1\rangle=c_{01}|0\rangle+c_{11}|1\rangle$. But this has a high risk of getting confused with multi-qubit basis states, so the answer above is probably best for a course. Aug 20 '21 at 0:03