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

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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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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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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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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 ($\Delta m=+1$) $$\vec{E}(z,t)= \vec{E}^{(+)}_0 e^{-i\nu t}+c.c. $$ ...
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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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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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Understanding the optimal approximate qubit cloning method

I'm trying to understand the operation used for optimal cloning of pure qubits states from the paper Optimal Cloning of Pure States by R. F. Werner. The paper describes the optimal cloning method $\...
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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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Convex combinations of states yielding a pure state

Wikipedia states that Geometrically, when the state is not expressible as a convex combination of other states, it is a pure state.[9] The family of mixed states is a convex set and a state ...
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How can I write a Gaussian state as a squeezed, displaced thermal state

I would like to write a Gaussian state with density matrix $\rho$ (single mode) as a squeezed, displaced thermal state: \begin{gather} \rho = \hat{S}(\zeta) \hat{D}(\alpha) \rho_{\bar{n}} \hat{D}^\...
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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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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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What are fragmented condensates?

It is defined that if more than one eigenvalue of the one-body density matrix are macroscopically occupied the condensate is said to be fragmented. $$ n^{(1)},n^{(2)},...=\mathcal{O}(\mathcal{N}) $$ ...
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Density matrix and entangled states

I am studying the density matrix formalism. I gather that: the trace of a density matrix, $tr(\rho)$ is always 1, if $tr(\rho^2) < 1$ we have a mixed state, otherwise a pure state, if $\rho$ ...
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What is the link between the density matrix and Hestenes' spinors in geometric algebra?

The density matrix (or state matrix) is a generalization of a wave function that is able to describe incoherent superpositions of an N-state system. It is often written as a matrix and observables are ...
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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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Superposition and density matrix. What are these states?

I just wanted to understand the following. Let's stay with the harmonic oscillator in QM, just to have an example at hand. First, there are all the different states for $n=1,2,...$. (Let's call them $...
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Can I usefully interpret a non-unital completely positive (CP) map as a cooling process?

Non-unital completely positive (CP) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily ...
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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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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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Lindblad equation solution

I have been trying to solve a Lindblad Equation and then thought about whether there is a closed form Lindblad Equation solution for most types. Googling hasn't lead me to anything useful. So, is ...
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How can all quantum measurement statistics be seen just as projective measurements on pure states?

Let $\rho$ be the density matrix for a system and let the POVMs be $\{E_m\}$ such that $\sum_i {E_m} = I$. The probability of getting the outcome $m$ is $\operatorname{Tr}(E_m \rho)$. The source I ...
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What kind on transformations can be applied on density matrices?

Completely positive trace preserving maps ( CPTP ) transform a valid density matrix to another, then why do we only talk about unitary transformations on density matrices ( $\rho \to U\rho U^{\dagger}...
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What is the reason for 2 qubits no longer being entangled after interaction with a causality violating qubit?

Background : I was reading the following paper on closed timelike curves ( CTC ) : Quantum Mechanics Near Closed Timelike Curves. The Deutsch consistency equation for CTC is $$\rho_{CTC}=Tr_{CR}( U \...
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Density operator time evolution in the path integral approach

I want to know how the density operator of a system evovles when we use path integral approach.
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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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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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reduced density matrix of multiparticle system

Let the state of a composite system is $|\psi_{i}\rangle$ then the density matrix is defined as, $\rho=\sum P_{i}|\psi_{i}\rangle\langle\psi_{i}|$ Consider a composite system of two particles and its ...
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Decoherence in the long time limit of density matrix elements

For a state $$ |\Psi(t)\rangle = \sum_{k}c_k e^{-iE_kt/\hbar}|E_k\rangle, $$ the density matrix elements in the energy basis are $$ \rho_{ab}(t) = c_a c^*_be^{-it(E_a -E_b)/\hbar} $$ How is it that ...
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Is it correct to represent a mixed state by a wavefunction?

Many sources (such as The Physics of Quantum Mechanics and the answers to this Physics.SE question) warn against conflating a mixed state where $|\psi\rangle$ is $|n\rangle$ with probability $p_n$, ...
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Density matrices & spin correlation

So I have two 1/2 spin systems A and B in a singlet state $|ψ>=\frac{1}{\sqrt{2}}(|\uparrow \downarrow>−|\downarrow \uparrow>)$ . The question is: If I measured B and got $S_{Bz}=\hbar/2$ . ...
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canonical ensemble density matrix numerical integration of the von Neumann equation

I am working with a numerically calculated Eigensystem of a given non-linear Hamiltonian. As a test I integrated Schrödinger equation for each eigenstate in time with Dormand Prince 54 and also Runge ...
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Is there a physical significance to non-normal states of the algebra of observables?

Quantum theory may be formalized in several different ways. Generally, the physical discussion of different states of a quantum system distinguishes pure and mixed states, and then subsumes both in a ...
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Density matrix in Quantum Statistical Mechanics

What is the connection between the density matrix in quantum statistical mechanics and the probability of being a particular state in classical statistical mechanics? It would seem that the elements ...
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Non-unqiue basis sets of reduced density matrix in quantum mechanics/decoherence

In Why decoherence solves the measurement problem by Art Hobson: $|\psi \rangle _{SA} = c_1|s_1 \rangle |a_1 \rangle + c_2 |s_2\rangle |a_2 \rangle$ which is a wavefunction that describes non-local ...
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How to find density matrix?

The Beam-splitter matrix is $ B = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1\\ 1 & -1 \end{pmatrix} $. I want to apply $a^{\dagger}_{1}a^{\dagger}_{2} |00\rangle_{12}$ as the input state for ...
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Continous and Discrete basis, Multiplication of Density Matrix and Hamiltonian

Suppose I have a wave function $\psi(x)$ in position basis. I can make a density function by simply multiplying $\psi(x)$ and its conjugate $\psi^*(x)$. If I operate the density matrix $\rho(x,y)=\...
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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 ...