Questions tagged [open-quantum-systems]
The study of open quantum systems is concerned with understanding and predicting the dynamics of quantum systems that are coupled significantly to their surroundings, leading to effects such as dissipation and decoherence.
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Problem with an extra term in the von-Neumann equation
I have recently started studying quantum systems with mixed states, and I have come across with the von-Neumann equation. I could derive it by making the time derivative of the explicit form of the ...
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Stuck while deriving the Lindblad Master Equation
I was following Quantum Markov Processes from the book The Theory of Open Quantum Systems by Breuer and Petruccione. In the section The Markovian Quantum Master Equation they proceeds to 'construct ...
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Please help regarding solving Schrodinger's equation in matrix form [closed]
In one of (the papers), I am reading on derivation of optimal conditions for photon antibunching, it is required to solve Schrodinger's equation using the following Hamiltonian (in the rotating frame) ...
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Why in 2-level system can a diagonal lindblad equation be used to describe decay, when $|0\rangle$ and $|1\rangle$ aren't energy eigenstates anymore?
Citing Wikipedia (https://en.wikipedia.org/wiki/Lindbladian), the Lindblad equation takes the following form:
\begin{align}
{\displaystyle {\dot {\rho }}=-{\frac {\mathrm {i} }{\hbar }}[H,\rho ]+\sum ...
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Factorization of density matrices
I'm currently reading through the following document about quantum noise and open quantum systems: https://courses.cs.washington.edu/courses/cse599d/06wi/lecturenotes13.pdf. On page 6 of the document, ...
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Does the Davies secular equation apply to infinite dimensional systems?
The original Markovian Master Equations paper by Davies from 1974 seems to only go into the case of finite dimensions. Sources like Petruccione don't specify the dimension.
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Why can we "wait for decay to the ground state quite generally"?
As it pertains to state preparation, but also quite generally, why should the method of waiting until decay to the ground state work at all?
Ballentine writes "It is possible to prepare the ...
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Confusion regarding the derivation of Lindblad master equation
I am reading theory of the master equation from Preskill's notes, section $3.5.2$. In the derivation, he writes
In the case of an open quantum system, Markovian evolution for the
infinitesimal time ...
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Coupling between harmonic oscillator and bath?
I have seen that in many experimental papers dealing with some form of oscillator coupled to a bath, people model system as $H = H_s + H_b +H_{sb}$ with
$$
H_s = \omega_s a^\dagger a, \quad H_b = \...
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Uniform losses commute with linear optics: how does it work?
In many papers about quantum optics and interferometry, it's assumed or said that "it's well known" that linear optics commutes with uniform losses. In particular if we have a beam splitter ...
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How to derive or understand the quantum detailed balance condition for Markov open system?
In the "On The detailed balance conditions for non-Hamiltonian systems", I learned that for a Markov open quantum system to satisfying the master equation with the Liouvillian superoperators,...
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Conditions for the existence of a steady state in time-driven system
Consider an open quantum system given by the Hamiltonian
$$H = H_B + H_S(t) + H_{SB}$$
with $B$ denoting the noninteracting bath, $H_S(t)$ the time-dependent noninteracting system and $H_{SB}$ is a ...
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Pushing a Hamiltonian part into dissipative part in Lindbladian
Suppose we have the following Lindbladian:
$$\mathcal{L}(\rho) = -\frac{i}{\hbar}[H, \rho] + \sum_\alpha L_\alpha \rho L_\alpha^\dagger - \frac{1}{2}\{L_\alpha^\dagger L_\alpha, \rho \}.$$
Suppose we ...
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Intuition behind the different collapse terms of the Lindbladian?
A common way to treat dissipative quantum systems is through the use of the Lindblad master equation. Compared to the Schrodinger equation, it has extra non-unitary collapse/jump operators that ...
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Is there an efficient way to execute a quantum channel using its Choi state?
Consider you are given a Choi state
$$
\sigma = (\mathcal{E} \otimes I) | \omega \rangle \langle \omega| \qquad {\rm with } \quad |\omega \rangle = \frac{1}{\sqrt{d}}\sum_{i} |ii \rangle \quad \textrm{...
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How to show that the Liouvillian fulfills $\langle A, \mathcal{L}B\rangle = \langle \mathcal{L}^\dagger A,B\rangle $?
How can I show that the Liouvillian superoperator $\mathcal{L}$ satisfies
$$
\langle A,\mathcal{L}B\rangle=\langle \mathcal{L}^\dagger A,B\rangle
$$
where $\langle A,B\rangle =\mathrm{Tr}(A^\dagger B)...
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Why energy-positivity?
In any relativistic quantum field theory, we require that the spectrum is bounded from below. The typical explanation is that this condition enforces the stability of the theory. However, to me this ...
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Why is $\frac{d}{dt}\hat{\rho}=\mathcal{L}[\hat{\rho}]$ a reasonable starting point in deriving the Lindblad master equation?
It is fairly simple to show that the Schrodinger equation is of the form,
$$\frac{d|\psi(t)\rangle}{dt}=-\frac{i}{\hbar}\hat{A}|\psi(t)\rangle$$
for some Hermitian $\hat{A}$,
from the assumption that ...
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What is wrong with decoherence? [closed]
One possible explanation of the quantum to classical transition, or in other words of why we don't see macroscopic quantum effects naturally, is environment induced decoherence.
Basically, the system ...
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Is projective measurement a channel that results from a unitary evolution on both the system and the apparatus?
I was researching the motivation behind introducing quantum channels and this is essentially what I've gathered.
Suppose we have two subsystems, the system we're interested in where states exist in ...
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Why does the fact that all quantum systems are open mean that no quantum state can be pure
I am teaching myself about open quantum systems and I am confused by the following statement on the wikipedia page about open quantum systems:
"The fact that every quantum system has some degree ...
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Norm of a jump operator
What is the restriction on the norm of the operator $L_k$ in the Lindblad master equation $\dot{\rho} = \sum_k L_k \rho L_k^\dagger + \frac{1}{2}\left\{ L_k^\dagger L_k, \rho\right\}$? Although there ...
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How to transform a Lindblad operator basis?
I'm trying to understand how to perform a unitary transformation on a set of traceless orthonormal Lindblad operators, following chapter 3.2.2 of The Theory of Open Quantum Systems by Breuer and ...
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Connection between Green's function and density Matrix
There are different approaches to solve the many-body problem of an open-quantum system. Just to mention two methods, there are the Equations Of Motion (EOM) and the Hierarchical Equations Of Motion (...
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Expressing non-Hermitian Dynamics in general and in the Heisenberg picture
Suppose I have an open system governed by a master equation
$$\frac{d}{dt}\hat{\rho} =-i\left[\hat{H},\hat{\rho}\right]+\gamma\left(2\hat{J} \hat{\rho}\hat{J}^{\dagger}-\hat{J}^{\dagger}\hat{J}\hat{\...
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Relating the Lindbladian to Kraus operator: why do we assume the specific Kraus: $K_0=I+L_0 dt$ and $K_{\alpha \neq 0}=\sqrt{dt} L_{\alpha}$
In open quantum systems, for a Markovian evolution, we can derive a Lindblad form for the evolution.
There is a way to relate this Lindblad form to the Kraus decomposition of the quantum map ...
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From Lindblad operators to Kraus operators: an explicit example of a dephasing noise model
I'm trying to understand how to obtain a set of Kraus operators from Lindblad master equations. For a $1$-qubit dephasing noise model, it is well-known that the set of Kraus operators is $\{ \sqrt{p}I,...
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Lindblad operators of $n$-qubits local dephasing noise process
I know that Lindblad operator for $1$-qubit dephasing quantum channel is $L = \sqrt{\gamma} \sigma_z$ so that the corresponding master equation is $\dot{\rho} = \sigma_z \rho \sigma_z - \rho$ (e.g., ...
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How to solve the eigenvalue problem of Matrix product operator (MPO) using Tensor network method?
I am new to the Tensor network approach. I need to solve the eigenvalue problem for a Matrix product Operator (MPO). What are some techniques, resources, softwares or packages available to do it? I am ...
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Lindblad equation from microscopic principles for free particles with momentum interactions
I'm rather familiar with the formalism of quantum master equations, but I'm struggling with deriving from microscopic principles the collapse operators for a particular case I need.
I consider two ...
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Does the wave function of system plus detector satisfy the Schrödinger equation?
Let $S$ be a quantum system and let $D$ be a detector. Suppose that $D+S$ does not interact with the environment. Now when $D$ makes a measurement of $S$, the wave function of $S$ collapses. Therefore,...
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Why does the Lindblad master equation in Heisenberg picture not preserve commutation relations?
From the book of Breuer and Petruccione [1], the Lindblad master equation for open quantum systems reads $\mathrm{d} \rho (t) / \mathrm{d}t = \mathcal{L} \rho(t)$, where $\mathcal{L}$ is the Lindblad ...
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Proof of differentiate form of dynamical semigroups
I am studying some basics of the pure mathematical background for open quantum systems from Angel Rivas`s book which is "Open quantum systems, an introduction".
Here is a theorem (Page 6, ...
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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}\...
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Why do physical quantum maps need to be completely positive? [duplicate]
It has been a real question for me why exactly for studying open quantum systems it is not sufficient for the dynamical maps to be positive and must be completely positive.
what is the physical ...
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Expansion of the interaction term in the microscopic derivation of the Lindblad equation
I'm reading The Theory of Open Quantum Systems by Heinz-Peter Breuer and Francesco Petruccione, and in chapter 3, I can't understand the decomposition of the interaction Hamiltonian:
We assume that $H=...
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CP-divisible in Markovian and non-Markovian
There is a definition that says if the decay rates are positive the dynamical map would be CP- divisible semi-group and Markovian. On the other hand, the non-Markovian occurs when at least one of the ...
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Can Gaussian states be entangled without two-mode squeezing?
The Duan Criterion, when written as a function of creation and annihilation operators $b$ and $b^\dagger$ depends only on $\langle b_1^\dagger b_1\rangle$, $\langle b_2^\dagger b_2\rangle$ and $\...
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Can Gaussian states be implemented with a classical system?
Gaussian states for $n$ quantum harmonic oscillators can be fully described by a $2n \times 2n$ matrix $\Theta_{ij} = \langle \delta \alpha_i \delta \alpha_j\rangle$ (and a displacement vector which I ...
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Why do bath correlations decay?
When deriving a Lindblad equation (for example Breuer chapter 3), one crucial assumption is that $\tau_b$, the reservoir correlation function decay time, is (in short) the smallest relevant time scale....
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What's the efficient numerical method to calculate the steady state of many-body quantum open systems?
I need to calculate the steady state of many-body quantum open system in cavity with Hamiltonian:
$$H=\frac{g}{\sqrt{N}}\alpha \sum^{N}_{i=1} (b_i a+b_i^\dagger a^\dagger )+\frac{g}{\sqrt{N}}(1-\alpha)...
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In an open quantum system, what is the justification for using a harmonic oscillator bath to represent the molecular environment in a solvent?
The Caldeira-leggett (CL) model is sometimes used to describe quantum mechanical effects in a system (like a biomolecule) immersed in a solvent. The Hamiltonian of the CL model consists of an ...
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Absorption spectrum of open quantum systems
I'm trying to understand the properties of continuous absoption spectrum of molecules in a solution using an oversimplified quantum mechanical argument.
First, let us model our isolated molecule in ...
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Cavity Input-Output Formalism: Physical significance and intuitive understanding
I have spent a lot of time trying to understand the input-output formalism for cavities. I sort of understand the idea
Fields inside an optical cavity(our system) will have losses because the mirrors ...
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Can reduced dynamics lead to a map that is not completely positive?
This question is a follow-up to this one.
The setup is the same as in that question. We consider a map from a certain set of density operators $\rho_S$ on a Hilbert space $\mathcal{H}_S$ to the ...
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How can an entangled initial state lead to non-positive reduced dynamics?
According to https://arxiv.org/abs/1206.3794, the standard treatment models the time evolution of open quantum systems as follows: starting with a system in the initial state $\rho_0$ on the Hilbert ...
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Collapse operators of two-level atom
Currently I am learning about the Lindbladian. I want to derive the optical bloch equations for a two-level atom interacting with monochromatic light from the Lindbladian. However I am having troubles ...
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Arbitrariness of Quantum Heat Current
Given a Hamiltonian $H$ for a closed quantum system, we know that the spectrum is invariant under any constant shift in energy $H'=H+c$. However, when talking about open quantum system where the ...
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Can we consider the Hamiltonian of a single qubit as zero?
I am studying the Daniel Lidar`s lecture notes about open quantum systems. In the part that I have already attached it here, it considers the Hamiltonian of the single qubit as zero to implement into ...
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To verify the completely positivity: about conditionally completely positive
I'm reading the paper Assessing Non-Markovian Quantum Dynamics, by M.M. Wolf (PRL 101, 150402 (2008), arXiv:0711.3174). It mentions how to decide whether a generator is a valid Lindbladian generator, ...
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