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

learn more… | top users | synonyms (1)

1
vote
1answer
28 views

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 ...
3
votes
1answer
185 views

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 ...
4
votes
1answer
161 views

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 ...
2
votes
1answer
64 views

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 ...
1
vote
1answer
48 views

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 ...
4
votes
1answer
64 views

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 ...
3
votes
2answers
78 views

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 ...
10
votes
1answer
311 views

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 ...
4
votes
4answers
208 views

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 ...
0
votes
3answers
83 views

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 ...
1
vote
1answer
417 views

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 ...
4
votes
0answers
81 views

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 ...
2
votes
2answers
123 views

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 ...
3
votes
2answers
190 views

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 ...
3
votes
3answers
199 views

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, ...
4
votes
0answers
95 views

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} | ...
0
votes
0answers
43 views

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 ...
2
votes
1answer
90 views

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, ...
3
votes
1answer
68 views

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 ...
0
votes
1answer
55 views

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 ...
24
votes
7answers
9k views

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 ...
1
vote
1answer
60 views

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 ($\Delta m=+1$) $$\vec{E}(z,t)= \vec{E}^{(+)}_0 e^{-i\nu t}+c.c. $$ ...
0
votes
1answer
41 views

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 ...
2
votes
1answer
57 views

2x2 Matrices that are not valid quantum states

Given a 2-dimensional Hilbert space, quantum states can be expressed as $2\times 2$ density matrices. In terms of the Pauli matrices, or Bloch representation, they can be written as \begin{equation} ...
1
vote
1answer
75 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 ...
4
votes
3answers
1k views

What is the physical interpretation of the density matrix in a double continuous basis $|\alpha\rangle$, $|\beta\rangle$?

(a) Any textbook gives the interpretation of the density matrix in a single continuous basis $|\alpha\rangle$: The diagonal elements $\rho(\alpha, \alpha) = \langle \alpha |\hat{\rho}| \alpha ...
1
vote
1answer
144 views

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 ...
3
votes
0answers
70 views

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. $$ n^{(1)},n^{(2)},...=\mathcal{O}(\mathcal{N}) $$ ...
0
votes
0answers
36 views

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 ...
0
votes
1answer
34 views

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 ...
0
votes
1answer
86 views

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: ...
0
votes
2answers
53 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?
0
votes
1answer
65 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 ...
3
votes
1answer
78 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 ...
0
votes
1answer
82 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 ...
3
votes
0answers
49 views

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 $\rho$ ...
2
votes
0answers
56 views

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 ...
0
votes
0answers
60 views

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 ...
0
votes
0answers
57 views

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 $p_n$, ...
0
votes
0answers
39 views

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 $S_{Bz}=\hbar/2$ . ...
-1
votes
1answer
59 views

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 ...
7
votes
3answers
230 views

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 ...
0
votes
0answers
37 views

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 ...
0
votes
2answers
195 views

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 ...
2
votes
0answers
100 views

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 ...
1
vote
2answers
127 views

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 ...
3
votes
3answers
273 views

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 ...
-1
votes
1answer
71 views

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 ...
8
votes
0answers
314 views

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}} ...