Questions tagged [master-equation]
19 questions
5
votes
1 answer
For how many different times do I have to know that $e^{tL}$ is a quantum channel to conclude that $L$ is of Lindblad form?
As first shown by Gorini, Kossakowski, Sudarshan and Lindblad given some linear map $\mathcal L:\mathbb C^{n\times n}\to\mathbb C^{n\times n}$, $e^{t\mathcal L}$ is a quantum channel for all $t\geq 0$ if and only if there exist $H$ Hermitian as well…
Frederik vom Ende
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5
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What does "generator" mean in the master equation?
I seem to read a lot of times that some materials called this $\mathcal{L}$ in the equation(Lindblad master equation) below as the generator:
$$
\mathcal{L} \rho=-i[H, \rho]+\sum_{\alpha}\left(V_{\alpha} \rho…
Sherlock
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4
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Is purity convex in time?
Is the purity $\mathrm{Tr}[\rho(t)^2]$ of a quantum state $\rho(t)$ that evolves according to a time-independent Lindbladian $\partial_t \rho = \mathcal{L}[\rho]$ convex in time $t$?
I suspect the the answer is "no" in general, but I wonder whether…
nlupugla
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4
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Distribution of density operators under Stochastic Master Equation
Stochastic master equations (SME) are used in studies of open quantum systems. The general form of an SME is:
\begin{align}
\tag{1} d\tilde{\sigma}(t) = - i [H, \tilde{\sigma}(t) ]dt + \frac{1}{2}\sum_{j=1}^d \left([L_j \tilde{\sigma}(t), L_j^*] +…
MonteNero
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votes
1 answer
What is "Lindblad Superoperator" in Stochastic Master Equation
I was reading a paper titled "Using a Recurrent Neural Network to Reconstruct Quantum Dynamics of a Superconducting Qubit from Physical Observations" and was confused about a stochastic master equation governing the evolution of the single-qubit…
C. Ardayfio
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1 answer
Show that if the Lindblad satisfy $\sum_\mu L_\mu L_\mu^\dagger=\sum_\mu L_\mu^\dagger L_\mu$ then $\rho\propto I$ is a fixed point of an evolution
How can we show that the Lindblad condition:
$$\sum_{\mu}L_{\mu} L_{\mu}^{\dagger} = \sum_{\mu} L_{\mu}^{\dagger}L_{\mu},\tag{1}$$
implies that $\rho \propto I$ is the fixed point of the evolution with the maximum entropy (this corresponds to the…
Sudhir Kumar Sahoo
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How to formulate the master equation for three systems?
I have a three composite system of the form $H_{\text{tot}}=H_{ab}\otimes H_c$ where the system $C$ is behaving as the dissipator or the environment (I can model it as a thermal bath). And it is coupled only to system $B$ but not $A$. While $A$ is…
Siddhant Singh
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What would a master equation describe for a Hamiltonian $H=\alpha 1 + \beta \sigma_x$?
Consider the following master equation:
$$
\partial_{t} \rho = -i [H, \rho ] + \gamma (\sigma_{-} \rho \sigma_{+} - \frac{1}{2} \sigma_{+} \sigma_{-} \rho - \frac{1}{2} \rho \sigma_{+} \sigma_{-})
$$
Here, $\sigma_{+} = |1 \rangle \langle…
phy_std
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votes
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Density matrix and State vector give different result in mesolve in QuTiP
qutip mesolve gives me different population evolve depending on that initial state is state vector or density matrix. And, in some situation, it gives me negative population. It doesn't make sense...
Does anyone encounter this problem?
Population…
eechiki
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2
votes
1 answer
Simulate dual Lindblad master equations in the Heisenberg picture in QuTiP
In QuTiP, it is possible to solve Lindblad master equations describing the time evolution of an open quantum system $\rho$:
$$
\dot{\rho}(t)=-\frac{i}{\hbar}[H(t), \rho(t)]+\sum_n \frac{1}{2}\left[2 C_n \rho(t) C_n^{\dagger}-\rho(t) C_n^{\dagger}…
francois-marie
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2
votes
1 answer
Notation for Lindblad operators
I was reading the paper Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation (arXiv). The claim is that universal quantum computation can be achieved using the dissipative approach. That is, we let…
MonteNero
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2
votes
1 answer
Nielsen and Chuang: Solving equation of motion for amplitude damping
I would like to know how to obtain a solution to the equation of motion given in Section 8.4.1 Master equations of Nielsen and Chuang, 10th edition.
The equation of motion that allows getting the quantum operation of amplitude damping is given…
MonteNero
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2
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1 answer
How to solve non-"cross-damping off" Linblad equation in QuTiP?
As I understand from the official QuTiP guidlines, it is only capable of solving "cross-damping off" Master Equation in form:
$\dot{\rho(t)} = -\dfrac{i}{\hbar}[H(t),\rho(t)] + \sum\limits_n\dfrac{1}{2}\left[ C_n\rho(t)C_n^{\dagger} -…
mesolver
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vote
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Unintended "decoherence" when evolving a three level system using qutip.mesolve
I am trying to simulate the evolution of a three-level system, using mesolve.
Strangely, the state seems to "decohere" without any collapse operators involved.
At the moment, I am just trying to calculate the evolution of a superposition state of…
danyudi
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1
vote
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QuTiP tutorial: How to derive the analytical solution to the expectation value of an operator for a system evolving by Lindbladian
I am following the simple tutorial below:
(https://nbviewer.org/urls/qutip.org/qutip-tutorials/tutorials-v5/time-evolution/003_qubit-dynamics.ipynb)
In this they look at single qubit with Hamiltonian $H = \frac{\Delta}{2}\sigma_{x}$ and 1 jump…
LieAlgebraGuy1999
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