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

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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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62 views

Density matrix from Wigner distribution

Density matrix or Wigner function can be defined from the other with Fourier (or inverse) transformation. equivalently the value of W(q,p) can be seen as the mean value of the displaced parity ...
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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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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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Complex vector on Block sphere [closed]

I've the following problem. Given this vector on a 3D complex space: $$\\\\ {\phi_{1}} = \begin{matrix}% 1/2(-1, & i\sqrt{2}, &1)^{T} \end{matrix}\\ $$ Is it possible to draw it on the ...
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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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40 views

Density matrices vs Pauli matrices

Studying quantum mechanics, I have suddenly come to the conclusion that Pauli matrices are essentially density matrices for spin systems. Does it make any sense or I have missed something?
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31 views

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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72 views

Harmonic oscillator with heat bath

I need to calculate the expectation value for a harmonic oscillator coupled to a heat bath using the trace method. I know that the density operator looks like: $$\rho = \frac{e^{-H / k_B ...
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69 views

How do we prove $P(a_{n})=Tr\{\rho|a_{n}\rangle\langle a_{n}|\}$ in a mixed state?

If we have a mixed state such that, with probability $P_{1}$ the system is in state $|\psi_{1}\rangle$ and with probability $P_{2}$ the system is in the state $|\psi_{2}\rangle$ How do we prove that ...
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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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Is density matrix really a description of 'state'? [closed]

Generally a density matrix is in fact a description of a set of equivalent (experimentally indistinguishable in linear QM) states. So there is no 1-to-1 correspondence between density matrix and ...
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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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How to define a non-thermal state? [closed]

I got a very vague question. A thermal state is defined by $$\rho=\frac{e^{(-\beta H)}}{Z_\beta},$$ where $Z$ is the partition function. I want do now calculations with "non-thermal states", but ...
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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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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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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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Trace representation of density matrix question [closed]

System $A$ and system $B$ form a composite system. https://en.wikipedia.org/wiki/Partial_trace I wonder why $\rho_{AB}$ cannot be represented as $(\text{tr}_{B}(\rho))\otimes ...
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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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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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Does this quote from my textbook imply that not all states are superpositions?

I read this at a book; The difference between bits and qubits is that a qubit can be in a state other than $|0\rangle$ or $|1\rangle$. It is also possible to form linear combinations of ...
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Definition of the “support” of the reduced density matrix

Some of the papers in condensed matter physics use the word "support" (space). For example, the following papers use the support especially for the reduced density matrix. ...
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Separability of density operators on tensor product spaces

Consider a composite system $\mathcal{H}=\mathcal{H}_{A}\otimes\mathcal{H}_{B}$ where $\mathcal{H}_{A}$ and $\mathcal{H}_{B}$ are Hilbert spaces of constituent components (say two qubits). Let ...
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Purity of a maximally mixed quantum state

The trace of the square of a density matrix(which is also called the Purity of the quantum state) is (lower)bounded by the inverse of the dimension of the Hilbert space and (upper) bounded by 1. I ...
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Density Matrix in Quantum Optics

I am studying laser physics and didn't get the whole idea of the density matrix (in this case for two-level systems). I know this is really basic so bear with me! I understand that the diagonal ...
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52 views

One-electron reduced density matrix: Argument for positive semidefiniteness

I cannot follow an argument for positive-semidefiniteness of the one-electron density matrix given in "Molecular Electronic-Structure Theory" by Helgaker/Jorgensen/Olsen. First some definitions: ...
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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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359 views

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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4answers
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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 ...
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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 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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Entropy change in Heisenberg picture

If we stick with Heisenberg picture where density matrix $\rho$ is constant, how do we account for entropy increase? I've read the answer to State collapse in the Heisenberg picture but I don't see ...
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1answer
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Bounds on dimension of a purification?

Let $\rho \in H_A$ be a density operator, $H_A$ is finite dimensioal, it is well known that $\rho$ has a purification in some larger hilbert space. Let $b$ be the minimum dimension for $H_B$ such ...
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Time dependence of the displacement operator

I am following the derivation of the master equation (and application of this) in these lecture notes. Unfortunately I do not follow the step of eliminating the driving terms of the harmonic ...
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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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Kubo formula for general observables

In the wiki page about Kubo formula, the expectation of some observable under weak time-dependent perturbation is derived. However, from my point of view, some crucial steps are missing. I did the ...
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What is the effect of squeezing on the Husimi phase space representation or Q-function?

The effect of the squeezing operator \begin{equation} S = e^{- r (a^2 + a^{\dagger 2}) / 2} \end{equation} on a Wigner phase space representation or W-function of a system with density matrix $\rho$ ...
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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 ...
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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 ...
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Why reduced density operator being same is necessary sufficient for no signalling?

Problem Statement : Two parties $A$ ( Alice ) and $B$ ( Bob ) ( in order ) share an entangled pair $\frac{1}{\sqrt{3}}(|00\rangle+|01\rangle +|11\rangle)$. Bob does a measurement in basis $\{ ...
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How to see validity of no signalling principles in case of entangled parties?

From what I understood the density operator $\rho$ is a mathematical tool which tells us about the probabilities of getting a particular output after measurement. I have two parties entangled with ...
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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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Why is $\langle \textbf R \rangle =Tr \rho R$ here $\rho$ is the state density matrix

I came across this, \begin{post} To each state there corresponds a unique state operator.The average value of a dynamical variable \textbf{R}, represented by the operator $R$ ,in the virtual ensemble ...
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Kraus operators + path integrals = Lindblad equation?

The other day our professor was talking about Kraus representation of density operator and the derivation of Lindblad equation. He told that this was related to the Feynman path integrals and that we ...
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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 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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How can I calculate the partial trace for a combined state of a pair of two-level atoms to get a reduced state? [closed]

Let's say I have a combined state of a pair of two-level atoms, $A$ and $B$, given by the density matrix: $$ \rho = \frac{1}{2}\mid g_A, g_B \rangle \langle g_A, g_B\mid + \frac{1}{2} \mid g_A, e_B ...