# Tag Info

### closeness between two unitaries on the bloch sphere

A unitary $U$ corresponds to a rotation on the Bloch sphere. Technically, there is a smooth map from $2 \times 2$ unitaries with determinant 1 (which form the group SU(2)) to $3\times 3$ rotation ...

### closeness between two unitaries on the bloch sphere

There are several ways to quantify the closeness of unitary operators. The best approach will be heavily dependent on context. The approach you laid out is close to an operator norm, which would look ...

### Map $n$ qubit state with complex amplitudes to $n+1$ qubit state with real amplitudes

TL;DR: The proposed map fails to be insensitive to the global phase. For example, it can tell apart $|0\rangle\equiv[1,0]^T$ from $|0\rangle\equiv[i,0]^T$ even though these two different mathematical ...

### Map $n$ qubit state with complex amplitudes to $n+1$ qubit state with real amplitudes

Call the operation you want to construct $D$ and call the qubit that ends up storing the real/imaginary distinction $q$. If I gave you $D$, you could apply $D$ then $Z_q$ then $D^{-1}$. The overall ...