# Tag Info

### Can the Bloch sphere be generalized to two qubits?

For pure states, there is a reasonably simple way to make a "2 qubit bloch sphere". You basically use the Schmidt decomposition to divide your state into two cases: not entangled and fully entangled. ...
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### Can the Bloch sphere be generalized to two qubits?

Since a spin $j$ irreducible representation of $SU(2)$ has a dimension $2j+1$ ($j$ is half integer), any finite dimensional Hilbert space can be obtained as a representation space of $SU(2)$. ...
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### Why is an entangled qubit shown at the origin of a Bloch sphere?

Let $(x,y,z)$ be a point in the unit ball with $x^2+y^2+z^2 \leq 1$. The state associated with this point is \begin{eqnarray*} \rho &=& \frac{1}{2} (I_2 + x \sigma_x + y \sigma_y + z \sigma_z)\...
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### Is there any online Bloch sphere simulator?

This doesn't really answer the question as it's not an online simulator. It might still be relevant though as it is a way to produce this sort of gifs if one has access to the software. It is ...
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### What's a vector in the Bloch sphere representation?

The components of the Bloch vector of a state are the expectation values of the X,Y and Z Pauli matrices in that state and it has to be a full three-dimensional vector to capture the interior of the ...
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### Why is an entangled qubit shown at the origin of a Bloch sphere?

The Bloch sphere only represents the state of a single qubit. What you’re talking about is taking a multi-qubit state, and representing the state of just one of those qubits on the Bloch sphere. If ...
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### Represent Hadamard gate in terms of rotations and reflections in Bloch sphere

but how about γ? Gamma doesn't show up on the Bloch sphere. It's a global phase. It's unobservable without conditioning the operation on a second qubit, in which case it turns into phase kickback ...
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### Drawing tangent vectors to the Bloch sphere with qutip

First of all, qutip is not a visualisation library, even though it does provide some visualisation functionalities, mostly leveraging ...
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### Is every single-qubit unitary just a rotation around some unit vector on the Bloch sphere?

TL;DR: Yes, ignoring the unobservable global phase, every single-qubit unitary corresponds to a unique rotation of $\mathbb{R}^3$ and vice versa. Single-qubit unitaries and rotations Let us first pin ...
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### How to obtain Y rotation with only X and Z rotations gates?

Single-qubit unitaries are just 3D rotations, multiplied by a phase. So in order to find the actual angles, you can resort to the theory of rotation matrices, in particular to Euler's rotation theorem,...
The Pauli-$Z$ gate maps $|0\rangle$ to $|0\rangle$ and $|1\rangle$ to $-|1\rangle$. For Bloch sphere representation, state of a qubit is written like (look at my previous answer for a detailed ...