# Tagged Questions

The density operator describes a quantum system in an (in general mixed) state.

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### Is the density operator a mathematical convenience or a 'fundamental' aspect of quantum mechanics?

In quantum mechanics, one makes the distinction between mixed states and pure states. A classic example of a mixed state is a beam of photons in which 50% have spin in the positive $z$-direction and ...
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### What is the entropy of a pure state?

Well, zero of course. Because $S = -\text{tr}(\rho \ln \rho)$ and $\rho$ for a pure state gives zero entropy. But... all quantum states are really pure states right? A mixed state just describes ...
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### What does the sum of two qubits tell about their correlations?

How much can I learn about correlations between two quits by measuring the sum of their values? What is the best way to formalize such a question? Below is my original, longer formulation of the ...
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### Majorana-like representation for mixed symmetric states?

Is there a generalization of the Majorana representation of pure symmetric $n$-qubit states to mixed states (made of pure symmetric $n$-qubit)? By Majorana representation I mean the decomposition of ...
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### Shape of the state space under different tensor products

I am currently studying generalized probabilistic theories. Let me roughly recall how such a theory looks like (you can skip this and go to "My question" if you are familiar with this). Recall: In a ...
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### Finding the matrix representation of a superoperator

I am trying to express superoperator (e.g. the Liouvillian) as matrices and am having a hard time finding a way to do this. For instance, given the Pauli matrix $\sigma_y$, how do I find the matrix ...
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Suppose we have $$\rho=p_1\rho_1+p_2\rho_2$$ Where $\rho_1$ and $\rho_2$ are density matrices with $p_1+p_2=1$ I'm trying to show this is also a density matrix If we let $$\rho_1=\sum_i^n p_{\... 2answers 297 views ### Is it possible to write a Density Matrix in the following form? Is it possible to write an arbitrary density matrix \hat{\rho} in the following form ?$$\hat{\rho} ~=~ \frac{1}{N} \sum_{\ell=1}^N \left|x_{\ell}\right\rangle \left\langle x_{\ell}\right|,$$... 2answers 193 views ### Probability distribution of a pretty-good measurement Let \rho_{XE} be a classical-quantum state. That is,$$ \rho_{XE} = \sum_{x}\Pr[X=x] \cdot |x\rangle \langle x | \otimes \rho_{x} $$where every \rho_{x} is a density matrix with \mathrm{Tr}(\... 1answer 128 views ### Can reduced density matrices of sub systems of an entangled composite system be different? In a 4-dimensional hilbert space, only 4 entangled states( normalized ) are possible ( if I am not wrong ), the bell basis. In each of the state in bell basis the reduced density matrix is \frac{I}{2}... 1answer 1k views ### Fermi-Dirac distribution derivation? I am trying to derive the Fermi-Dirac statistics using density matrix formalism. I know that$$<A>= Tr \rho A.$$So I started from$$<n(\epsilon_i)>= Tr \rho n(\epsilon_i)=\frac {1}{Z} ...
Let $\rho = \begin{bmatrix}\ 1&0 \\ 0&0 \end{bmatrix}$, $\rho' = \begin{bmatrix}\ 0&0 \\ 0&1 \end{bmatrix}$, $\rho'' = \dfrac{1}{2}\begin{bmatrix}\ 1&1 \\ 1&1 \end{bmatrix}$ (...
Suppose we have a qubit in state $| \Psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$ Suppose we expose this to decoherence, which we will express as the state $| R \rangle$ such that | 0 \...