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Signal coherence/correlation vs quantum coherence

In general, I understand a signal $s(t) \in \mathbb{C}$ is called "coherent" when it has a large autocorrelation function. A pair of different signals $s(t)$, $r(t)$ can also be "coherent" if their ...
1
vote
0answers
47 views

Quantum Coherence in a Two-level System in the Density Matrix Formalism

Dealing with semiclassical light-matter interaction, in particular the interaction between an electromagnetic field and a two level system using the density matrix formalism, I learned that the system ...
1
vote
2answers
90 views

How do I plot the decoherence of an open system from its density matrix?

If I have a two qubit state interacting with an environment that will decohere it, how do I model the decoherence from the density matrix? For example, if I start with some state $\Psi(0)=|0>_1|1&...
1
vote
2answers
291 views

What is the importance of a diagonal density matrix after measurement/decoherence?

Let $|\psi_{SA}\rangle$ be the state of a system and an apparatus, for example an electron spin and a Stern-Gerlach apparatus. If $|\psi_S\rangle=\alpha|\uparrow\rangle+\beta |\downarrow\rangle$ ...
1
vote
2answers
432 views

Dirac delta function property in a scattering proof

I'm studying the proof for the decoherence of the off diagonal elements of a density matrix through scattering with the environment and I'm stuck at a certain point: My problem is A1.14 relation. (A1....
0
votes
1answer
124 views

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}, ...
1
vote
1answer
827 views

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 ...
1
vote
1answer
236 views

Solving for the density operator in the quantum Brownian motion master equation

I want to solve for the density operator in the quantum Brownian motion master equation, \begin{align} \begin{aligned} \frac{d\rho_S(t)}{dt}=&-\left(\frac{i}{\hbar}\right)\Big[H_S+\frac{1}{2}M\...
0
votes
0answers
72 views

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 ...
6
votes
1answer
2k views

Coherences in the density matrix

It is said that the off-diagonal elements of density matrix are "coherence". When a system interacts with its environment the off-diagonal elements decay and the final density matrix is the diagonal ...
9
votes
6answers
1k views

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 ...
4
votes
1answer
1k views

The effect of Quantum Decoherence on density operators

Suppose we have a qubit in state $| \Psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$ Suppose we expose this to decoherence, which we will express as the state $| R \rangle$ such that $$| 0 \...