# What are the standard eigenvalues in $\mathbb{C^2}\otimes\mathbb{C^2}$?

In $\mathbb{C^2}$, we generally take $+1$ and $-1$ as the standard eigenvalues, that's what Pauli-X, Pauli-Z measurements, etc will give us. Is there a similar standard while measuring in the Bell basis and the computational basis in $\mathbb{C^2}\otimes\mathbb{C^2}$?

Of course, the actual eigenvalues don't matter, as long as we are talking about the same resolution of identity, but I was just wondering if there was a convention.

• What do you mean by C2? – Josu Etxezarreta Martinez Jun 29 '18 at 14:17
• @JosuEtxezarretaMartinez, C2 is complex 2D space, or the space enough to describe 1 qubit. C2*C2 is for 2 qubits. – Mahathi Vempati Jun 29 '18 at 14:29
• I think need to be careful about which symbols you're using for this. I believe the convention is to use a tensor product symbol (\otimes in LaTeX) if you mean the product Hilbert space of two qubits, whereas I would read C_2 x C_2 as the space of 2 x 2 complex matrices, or what is conventionally written as C^{2 x 2}. – SLesslyTall Jun 29 '18 at 16:29