Questions tagged [density-matrix]

A density matrix is a matrix that can be used to describe a quantum system in a mixed state, a statistical ensemble of several quantum states. This should be contrasted with a single state vector that describes a quantum system in a pure state.

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Show that $I = \frac{\rho + \sigma_x\rho\sigma_x +\sigma_y\rho\sigma_y + \sigma_z\rho\sigma_z}{2}$ for all states $\rho$

I am trying to show that for any qubit state p, the following holds: $$I = \frac{\rho + \sigma_x\rho\sigma_x +\sigma_y\rho\sigma_y + \sigma_z\rho\sigma_z}{2}$$ I have tried different manipulations,...
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Can an ensemble of pure states give probability less than 1?

I am calculating the reduced density matrix of a bipartite system, I ended up getting that it was the sum of two density matrices of pure states each with a probability $1/3$. My understanding was ...
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What does it mean geometrically (in terms of vectors in the Bloch sphere) if the commutator of two density matrices $ρ_1$ and $ρ_2$ vanishes?

When the commutator of two operators vanishes then we can measure one without affecting the other. I'm not sure how this translates in the case of density matrices. If the density matrices are ...
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Increasing the von Neumann entropy despite the measurement?

Background Assume we have a density matrix $\rho$ of a sub-ensemble. However, we have an imperfect measuring instrument. While it does perform a measurement, we do not know exactly when it performs ...
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Need some help with Purity calculation

maybe you could help me a little about my calculation of a quantum pure state with purification. I have this density matrix: \rho= \begin{pmatrix} 0.4489 & 0.2304 & 0.2162 &...
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Computation of a reduced density matrix

On wikipedia, the article on quantum entanglement gives an example of the computation of a reduced density matrix. I would like to understand precisely what's going on with the computation. First the ...
I'm trying to find the steady-state of a master equation, $$\dot{\rho}(t) = \mathcal{L}\rho(t),\tag{1}\label{1}$$ In the form where we vectorise the density matrix and matrixify (??) the Liouvillian ...