# Questions tagged [density-operator]

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

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### Differences between pure/mixed/entangled/separable/superposed states

I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum ...
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### What is quantum entanglement? [closed]

What is quantum entanglement? Please be pedagogical. Edit: I have updated my background under my profile.
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### Are there more entangled states or non-entangled ones?

I'm trying to understand entanglement in terms of scarcity and abundance. Given an arbitrary vector $v$ representing a pure quantum state of, say, dimension 4, i.e. $v \in \mathcal{H}^{\otimes 4}$, ...
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### How does a state vector be projected onto an eigenspace after measurement

In http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Degenerate_spectra, it is said that If there are multiple eigenstates with the same eigenvalue (called degeneracies),..., The ...
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### Is it possible to go from the Master Equation formalism to Heisenberg-Langevin equations

If I have derived a master equation (e.g. in the Lindblad form) and solved for the density matrix, $\rho(t)$ I can get the mean value of an operator, A as: $<A> = \mathrm{Tr}A\rho$. But ...
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### Is there a clear and intuitive meaning to the eigenvectors and eigenvalues of a density matrix?

Is there a clear and intuitive meaning to the eigenvectors and eigenvalues of a density matrix? Does a density matrix always have a a basis of eigenvectors?
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### Off-diagonal terms in density operator of pure state

The density operator for a pure state $| \psi \rangle = \sum c_i | \psi_i \rangle$ (where $\{|\psi_i\rangle\}$ is a basis) is: $$\rho = \sum_{i,j} c_j^* c_i | \psi_i \rangle \langle \psi_j |$$ On ...
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### Does the wave function/density state actually exist?

I have been reading with interest the debates here on whether the wave function/density state actually collapses or not, or whether it is subjective Bayesian or objective with actual complex numbered ...
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### Takhatajan's mathematical formulation of quantum mechanics

So I began skimming L. Takhatajan's Quantum Mechanics For Mathematicians, and saw the mathematical formulation of QM that he uses (page 51). (The PDF file is available here.) I've only taken a basic ...
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### Relationship between the Lindblad Equation and Redfield Equation

Both the Lindblad and Redfield Equation both model the open quantum system dynamics given a Hamiltonian and some operators. What is the relationship between the two equations? How can they transformed ...
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### States versus ensembles in quantum mechanics

In quantum mechanics, we talk about (1) vectors, (2) states, and (3) ensembles (e.g., a beam in a particle accelerator). Suppose we want to translate this into mathematical definitions. If I'd never ...
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### What information does the Von Neumann entropy give for mixed states?

Von Neumann entropy is defined as $$S=-\mathrm{Tr}\left(\rho \ln\rho\right)$$ It can be used to measure the entanglement between two sub-systems, provided that the total system is in pure state. ...
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### Definition of Entanglement

The definition of quantum entanglement, found on the internet and the literature is: On a bipartite system $\mathcal{H}_A \otimes \mathcal{H}_B$, let $\rho$ be a mixed state. It is said to be ...
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### Why do populations only change in second order of the driving field?

In the field of quantum optics when solving master equations it is well know that the populations1 are constants to linear order in the driving field. I.e. weak driving fields will only affect the ...
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### Classical and quantum correlations in bipartite system

I would like to know how to answer following questions: Is there classical/quantum correlations in given bipartite pure/mixed state? I have gathered several definitions. Some of them (it seems) ...