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

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How is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now consider state $\left|...
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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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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 the actual meaning of the density operator?

I am not able to understand the definition of the density operator. I know that if $V$ is a vector space and if I have $k$ states belonging to this vector space, say $|\psi_{i}\rangle$ for $1\le i\le ...
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Seemingly a paradox on the eigenstate thermalization hypothesis (ETH)

In the research field of Many-body Localization (MBL), people are always talking about the eigenstate thermalization hypothesis (ETH). ETH asserts that for a isolated quantum system, all many-body ...
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What is the difference between general measurement and projective measurement?

Nielsen and Chuang mention in Quantum Computation and Information that there are two kinds of measurement : general and projective ( and also POVM but that's not what I'm worried about ). General ...
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How to write a generic density matrix for multi qubit system

I was reading the paper device independent outlook on quantum mechanics. The author defines a generic two qubit density matrix as $$ \rho=\frac{1}{4}\left( I \otimes I + \vec{r_{\rho}} \cdot \vec{\...
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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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Density matrix formalism

The density matrix $\hat{\rho}$ is often introduced in textbooks as a mathematical convenience that allows us to describe quantum systems in which there is some level of missing information. $\hat{\...
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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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How to connect these two formulations regarding the need for a density matrix in quantum mechanics?

I found these two formulations: The density matrix is: 1) "needed if we consider a system that is part of a larger closed system." 2) "needed for a system to be ...
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What is the physical meaning of the Lindblad operator?

I read the wikipedia article on the Lindblad operator, but I still don't understand what this operator is supposed to describe. I therefore considered setting up an example in order to get the idea. ...
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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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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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Proving the unitary relation of ensemble decompositions

In my class it was told that ensemble decompositions of a density operator $\rho$ are not unique, but that the ones that exist are related by a unitary operator. I'm trying to prove this, but I get ...
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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} ...
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Normal Ordering and Smearing

I read on Wikipedia two different descriptions of the "Husimi-Q representation." One is that it is the Wigner function convolved with a Gaussian, which in particular results in a positive definite ...
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How does one compute the state of a quantum system following imperfect measurement?

Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$. I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
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Link Between the Density Operator and the Partition Function and Boltzmann Distribution in Quantum Statistical Mechanics

I have a very limited knowledge of statistical mechanics, but I seem to running into some related concepts for my background readings for the research project this summer. For example, see the ...
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What sort of operations can be applied on a Hilbert spaces?

I was reading the paper No Universal Flipper for Quantum States. In this paper they have tried to prove by contradiction that a universal flipping machine cannot exist. By flipping I mean if I have a ...