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

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SU(2) Coherent State and Probabilities

The SU(2) Corherent State for a for more than 1 two level system is given by: $$ | \eta, J \rangle = (1 + |\eta|^2)^{-J} \sum_{m=-J}^{J} \sqrt{\binom{2J}{J + m}} \times \eta^{J + m} |J, m \rangle, ...
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Entanglement of bi- and tripartite pure and mixed states

since I'm not sure on how to find out whether a system is entangled or not I thought about examples that could clarify the whole thing. first example: system is in the state $\rho=1/2 (| 000 \rangle \...
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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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expectaction value of coordinates on bloch sphere under special time evolution

We consider an example in which the time evolution of a system is given by the following density matrix $\rho(t)=\frac{1}{a_0+c_0}\begin{pmatrix} \eta^2(t)a_0 & \eta(t) b_0\\ \eta(t)b_0^{*} &...
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Heisenberg XXX time evolution operator for three qubits

I've a problem to reproduce the result in equation (4) on page three of this paper: http://arxiv.org/abs/0802.2588. So far I've understood that they apply a Heisenberg XXX interaction between 2&4,...
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Schrödinger's cat and the difficulty of macroscopic superposition state

The Schrödinger's cat was regarded as peculiar since we seldom encounter a superposition state in macroscopic scale: $$ \mid \mathrm{dead \,\,cat} \rangle + \mid \mathrm{alive \,\, cat}\rangle $$ We ...
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Using open system dynamics to define a quantum state

Background The density matrix of a closed quantum system with Hilbert space $\mathscr H$ evolves according to the von Neumann equation \begin{align*} i\hbar\dot\rho=[H,\rho]. \end{align*} Given a ...
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Meaning of the Reduced Density Operator

I am confused about what it is exactly that a reduced density operator describes. To illustrate, I came across the following seemingly paradoxical argument. Consider a bipartite system $AB$, ...
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Quantum master equation and off diagonal terms

I have a couple of related questions What is exactly the difference between the quantum master equation and the regular master equation? My understanding is that the normal master equation is used ...
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Density operator - Coherence relativ to a different basis

Consider the density matrix of the pure state $\left|\psi\right>$. Relativ to the basis, whose eigenvector is $\left|\psi\right>$, there are no coherences. Do a basis transformation and show ...
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Examples of Matrix Product State(s)

Matrix product states(MPS) is a way of representing a (many-body) wavefunction. The method has been described in, https://arxiv.org/abs/1008.3477 However, would it be possible to see a concrete ...
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On what conditions is a matrix a density matrix (of a pure state)?

I've been reading Weinberg's Lectures on Quantum Mechanics and the topic of the density operator (or density matrix, whatever you may call it) baffles me. Basically we have, $\hat{\rho}=\sum_ip_i\...
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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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how to get the matrices in partial trace

Good day, I want to ask the matrix that obtained from this link How to take partial trace?. answer from @Nontriviality below In principle what you do is to multiply the square matrix by rectangular ...
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Reduced density matrix

During a course on quantum mechanics we've been talking about density matrices. Now I came across the following exercise. Consider a two spin $\frac{1}{2}$ systems, labeled 1 and 2. Calculate: ...
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Two qubits system in polar co-ordinates

I know that I can write a single qubit state in terms of polar co-ordinates $(r,\theta,\phi)$ on a Bloch sphere. \begin{equation} \rho = \begin{pmatrix} \frac{1+r \cos\theta}{2} &\frac{r \exp(-i\...
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In quantum double slit experiment what is the state vector or density matrix of the electron after the electron passes through the two slits?

Also I would like to confirm my thinking on quantum double slit experiment. Before it passes through the two slits (slit 1 and slit 2), is the electron state vector $\frac{1}{\sqrt{2}}\left(\left|...
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Probabilities with the Density Matrix

The density matrix of the system is given by: $$ [\rho_{S}(t)]_{mn} = [\rho_{S}(0)]_{mn} e^{-i\omega_{0}(m - n)t} e^{-i \delta(t)(m^2 - n^2) - \gamma(t)(m - n)^2}, ...
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How to calculate the partial trace [duplicate]

Can anyone help me in explaining how this example below get the reduced density matrix from the density matrix in bipartite system. $$\rho =\frac{1}{4}\begin{pmatrix} 1 & 1 & cos(\frac{\alpha}...
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Reduced Density operator in matrix form

I already read book of Quantum Computation and Quantum Information by Nielsen and Chuang according to reduced density operator and I already understand how to do the reduced density using Dirac ...
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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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If an isolated quantum system consists of only one particle, is it possible for it to be in a mixed state?

Mixed states are defined as the statistical ensemble of pure states. Classically, I understand the word, "statistical" referring to a system with a large number of microscopic particles. So if I go ...
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Does Unitary operator take a pure state to a pure state or can it take a pure state to a mixed state? [closed]

Does Unitary operator take a pure state to a pure state or can it take a pure state to a mixed state? I think so but why? I assume the Unitary operator acts on a pure state only.
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Dirac notation - trace of product of (bipartite) density matrices

I'm getting confused by the Dirac notation. Suppose I have the following two objects. $$\rho = \sum_k p_k (\rho_A \otimes \rho_B) = \sum_k p_k |k \rangle \langle k | \otimes |k\rangle \langle k | ,$$...
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Density matrix: error with diagonalization claim and fixing it

On page 174 of Townsend's "A Modern Approach to Quantum Mechanics", 2nd edition, it says the following: "For a mixed state, one for which $p_k$ is the probability that a particle is in the state $|\...
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Questions involving seperable states

I'm reading Mark Wilde's book Quantum Information Theory, and I'm stuck on two parts. I'm unable to prove: The state $\sum_{z} p_{Z}(z) \; \rho_z \; \otimes \sigma_z $, where $\rho_z$ and $\sigma_z$ ...
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Undergraduate quantum book treating density operators, mixed states, and entanglement [duplicate]

I'm working on a project on quantum measurement theory - in particular, relating to the quantum Zeno effect - over the summer. Right now, I'm in the process of doing background readings that'd enable ...
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Equivalence condition of lindblad operators

So from Nielsen and Chuang th. 8.2 we know the equivalence condition of Kraus operators (quantum operation) What is the equivalence condition of lindblad operators of master equation?
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What is an incoherent state?

I am reading through a recent paper which speaks frequently of "incoherent states" without ever defining what such a state is. I gather from the context of the paper that it has something to do with ...
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Can every density operator be written as an outer product of two vectors?

I have a feeling this is a very basic question. I apologize if it is. Using Dirac's notation, can every (mixed) density operator $\rho_A$ of system $A$ be written as the ket-bra (outer) product $|a_1 ...
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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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Prove the solution of von Neumann equation will never stabilize if Hamiltonian and initial density matrix commutes

Given von Neumann equation $$\frac{d}{dt} \rho(t) = -i [H, \rho(t)] = -i e^{-iHt}[H, \rho(0)]e^{iHt}.$$ If we know that $[H, \rho(0)] \neq 0$, how do we prove in details the solution of von Neumann ...
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How does one describe a state with a density matrix after measuring position?

My question is about position measurement in non relativistic quantum mechanics. I've been taught that when you measure the value of an observable for some state of a system described by $|\psi\rangle$...
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Density Matrix representation of excited atoms

I'd like to get an answer to this question from someone who knows his density matrix theory. I want to compare two different systems and ask how their density matrix representation looks. First look ...
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Diagonalisation: Schmidt vs eigenvalue - when to use which?

In physics we encounter diagonalisation of matrices or operators in a variety of areas. But there are different kinds, the main two being Schmidt decomposition and eigenvalue diagonalisation. The two ...
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Two definitions of the density matrix?

There seems to be two different definitions of definitions of density matrices in Physics. In Quantum Information we define a the density matrix associated with a wave function $ | \psi \rangle$ as $...
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A seemingly paradox for Eigenstate Thermalization Hypothesis (ETH)

ETH states that for a system, all of its eigenstates thermalize. To be more specific, consider an energy eigenstate of the full system $H|n\rangle=E_n|n\rangle$. If the full system is in this ...
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What is the qualitative difference between quantum superpostion and mixed states? [duplicate]

As I understand it, if one has a complete knowledge of the state of a quantum system (insofar as one knows the statistical distributions of all the observables associated with the state) then one can ...
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Quantum computing entanglement dimensions question

While trying to understand the basics of how quantum computers work, I recently read this statement. "...consider that single-qubit states can be represented by a point inside a sphere in 3-...
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Completely positive maps and symmetric states

Let $\mathcal{N}$ be a completetely positive trace preserving map (aka a quantum channel) acting on a finite dimensional system $\mathrm{A}$, and let $\pi$ denote the maximally mixed state on $\mathrm{...
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Physical meaning of $Tr(\rho ^2)$

If $\rho$ is the density matrix of a system then $Tr(\rho ^2) \leq 1$. If the equality holds the system is in a pure state and it is in a mixed state otherwise. But, what is the physical meaning of $...
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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}(\...
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Difference between DMRG (density matrix renomalization group) and MPS (matrix product states)?

I am learning DMRG recently. I noticed there are many papers both in the DMRG approach and MPS (such as variational matrix product state (VMPS) by F.Verstraete and J.I.Cirac) approach. In my eyes, ...
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Berry phase with density matrix approach

Berry phase, coming from Schrodinger equation, has well known form in terms of closed integral $$\gamma = \int_C A(\xi) d\xi $$ with Berry connection $$A(\xi) = i < \psi(\xi) | \partial_{\xi} | \...
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the density matrix in QFT on a cylinder

My question regards the density matrix in quantum field theory on a cylinder. The partition function is given by $Z=\text{Tr} e^{-\beta H}$. The elements of this thermal density matrix become \begin{...
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Can mixed states be treated in the second quantization formalism? [closed]

In the first quantization formalism, mixed states can be handled using density matrices. When treating many-body quantum systems however, the second quantization formalism often comes handier, ...
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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 to represent a Liouville projection superoperator in Hilbert space?

Is there a general way to represent a Liouville projection operator in Hilbert space, or can they take on any form so long as they satisfy the required properties of a projector? e.g. The thermal ...
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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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How to include temperature effect in optical bloch equations (optical pumping)?

My problem is about the optical pumping of Alkali atoms by circularly polarized pump light. Consider a circular polarized light ($\Delta m=+1$) $$\vec{E}(z,t)= \vec{E}^{(+)}_0 e^{-i\nu t}+c.c. $$ ...