# Questions tagged [density-operator]

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

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### One-body entropy?

In theoretical studies of Bose-Einstein condensates, it's common to look at the one-body density matrix: $$n_{ab}=\langle\hat{c}_a^\dagger\hat{c}_b\rangle$$ where the $\hat{c}_j$ are annihilation ...
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### Multiplying inner products in QM

Getting introduced to mixed states in QM, I have trouble with a proof. In particular there was a line where multiple quantum states $\Psi_i, \Psi_j$ and an arbitrary base $n$ in Hilbert space was ...
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### non-pure states

I understand that states are associated with a state operator with certain mathematical properties. There is a subset of states, called pure states, that are represented by a state operator of the ...
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### Proof that $\langle \dot{O} \rangle = \text{Tr}(\dot{\rho}O)$

I'm reading a paper ([PRB],[arXiv]; first paragraph of section IV) that uses the identity $$\langle \dot{O} \rangle = \text{Tr}(\dot{\rho}O),$$ where $\rho$ is the density matrix, and $O$ is an ...
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### What is the interpretation of a non-diagonal density matrix?

Suppose an ensemble of a spin $\frac{1}{2}$ particle in the $S_z$ basis is described by a diagonal density operator $$\rho=w_{11}|+\rangle\langle+|+w_{22}|-\rangle\langle-|$$ where $w_{ii}$ are real ...
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### Three dimensional visualization of a qutrit

My question is in reference to the paper "Three dimensional visualization of a qutrit"(https://arxiv.org/abs/1601.07361). The author's start with a symmetric two qubit density matrix written in the ...
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### Density operator diagonal terms during decoherence

On page 7 of this paper by Sebens and Carroll they discuss the diagonal terms of the reduced density matrix during decoherence. I am very confused. I thought the diagonal terms are the only ones that ...