New answers tagged unitarity
2
votes
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 ...
- 6,596
2
votes
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 ...
- 3,352
2
votes
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 ...
- 20k
4
votes
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 ...
- 32.5k
3
votes
Map $n$ qubit state with complex amplitudes to $n+1$ qubit state with real amplitudes
This will violate unitarity of the transformation $U$. Consider states
$$\begin{bmatrix}\frac1{\sqrt2} \\ \frac1{\sqrt2}\end{bmatrix} (b=d=0)$$
and $$\begin{bmatrix}i\frac1{\sqrt2} \\ i\frac1{\sqrt2}\...
- 8,625
1
vote
Sufficient conditions for a single-qubit unitary to be the identity
Another way of phrasing it is "if $U$ maps every computational basis state to itself, such that all the computational basis states have the same global phase, then $U$ is identity, up to a global ...
- 54.5k
3
votes
Accepted
Sufficient conditions for a single-qubit unitary to be the identity
TL;DR: The premise - that $U$ which fixes elements of every basis may fail to be the identity - is false.
If a unitary $U$ fixes elements of every basis then in particular it fixes every vector and $U=...
- 20k
2
votes
Conditions for entangling $A$ with $C$ via an interaction on $AB$
This is not a fully characterised solution, but perhaps you will find it helpful...
We start by writing the initial $|\psi\rangle$ in its Schmidt basis,
$$
|\psi\rangle=\alpha|00\rangle+\beta|11\...
- 54.5k
2
votes
Conditions for entangling $A$ with $C$ via an interaction on $AB$
This isn't a full solution. More a way to reduce the problem in a more general one, and possibly pinpoint the difficult question that needs answering.
Let's assume $\rho_A$ is pure, $\rho_A\equiv |\...
glS♦
- 22.9k
2
votes
Accepted
What are the possible channels preserving purity of all pure input states?
TL;DR: The unitary and reset channels are the only ones that return pure output for every pure input. That's because under Stinespring dilation the requirement that $\Phi$ return pure output for every ...
- 20k
0
votes
Unitarity of a matrix in the EPR experiment
The key thing is that the two eigenvectors of $\vec{v}\cdot\vec{\sigma}$ are orthogonal. So if you create a matrix such as
$$
U=|a\rangle\langle 0|+|b\rangle\langle 1|,
$$
(this is technically the ...
- 54.5k
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