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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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Correlation function of a two-level quantum system coupled to a thermal bath

I am trying to quantify the temporal correlations of observables in an open quantum system, i.e. calculate a quantity of the type, \begin{equation} \langle n(t) n(t') \rangle - \langle n(t)\rangle \...
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Positive Constant in Lindbladian

Consider the following Lindbladian $$ L \left[X \right] = i \left[H, X \right] + \gamma \left( 2QXQ - \left(Q^2X + XQ^2 \right) \right), $$ where X is observable, in other words, Heisenberg picture. ...
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How can the Lindblad master equation model decoherence?

In some references that I have read, a crucial assumption in deriving the Lindblad master equation is that the system and environment remain separable for all time. Hence, the system and environment ...
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How to obtain "canonical form" of the following master equation?

I am following this paper (arXiv). The master equation given on page 4 (top left) reads: \begin{align} \dot{\rho} &= [2\gamma(t) + \bar{\gamma}(t)] [2 \sigma_x \rho \sigma_x + 2 \sigma_y \rho \...
phy_std's user avatar
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Jensen's inequality on (super)operator exponential

Let us define the expectation value $\langle A\rangle_{\rho}$ of a superoperator $A$ over a density matrix $\rho$ as $(\rho, A(\rho))$, where the scalar product between operators reads $(O_1,O_2):= Tr[...
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Does the Born quantum master equation preserve positivity?

The Born quantum master equation (QME), $$ \frac{d \rho}{d t} = -g^2\sum_{\alpha,\beta} \int_{0}^{t} d\tau \mathcal{B}_{\alpha\beta}(\tau)[A_\alpha(t),A_\beta(t-\tau)\rho(t-\tau)] +h.c. $$ is a ...
Daphne's user avatar
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Are $\mathcal{PT}$-symmetric Hamiltonians dual to Hermitian Hamiltonians?

I was reading this review paper by Bender, in particular section VI where they show that, despite $\mathcal{PT}$-symmetric Hamiltonians not being hermitian, they can have a real spectra. They go on ...
FriendlyLagrangian's user avatar
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Quantum systems with steady states: does a system always approach the steady state as it evolves?

Say we have a quantum system whose dynamics results in there being a steady state. For example, it may be described by a Linblad master equation with several opposing dissipators. It is obvious that ...
hendlim's user avatar
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Correlation functions zero for repeated creation or annihilation operators [duplicate]

In the derivation of the damped harmonic oscillator, at some point, see for instance here one has to compute certain correlation functions for the bath of harmonic oscillators in thermal equilibrium. ...
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Interpretation of a stochastic Schrodinger equation

Suppose we have a linear stochastic Schrodinger equation (SDE) describing the evolution of a system in a finite-dimensional Hilbert space: $$ d\psi(t) = \left(-iH(t) - \frac{1}{2}\sum_{j=1}^dR_j^{\...
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Relationship between decay rate and stationary state for the Lindblad Equation

I would like to know what is the role of the decay rate $gamma$ in the Lindblad equation written in the diagonal form \begin{equation} \dot{\rho}(t)= i[H,\rho(t)]+\gamma\sum_{\alpha}L_{\alpha}\rho(t)L^...
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What is the difference between a Lindbladian and a Liouvillian in open quantum systems?

As far as I know, when we try to write the Lindbladian equation in a generalized nice operator basis we get Liouvillian. Is this correct? What are the differences between them?
Rishwi Thimmaraju's user avatar
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Swap operation in a Radiative Random Unitary Circuit

In ref PhysRevLett.131.220404, the author have studied the scrambling in a Radiative Random Unitary Circuit (RUC) -- a RUC that exchanges qubits with an environment at a rate $p$. It might perhaps be ...
Young Kindaichi's user avatar
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Displacement operator and phase space

I read a paper on open quantum system, it's about non-Markovian process with memory effects. They describe a generic model of two qubits interacting with correlated multimode field. They describe the ...
Yohay Halfon's user avatar
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Decoherence model of two qubits interacting with correlated multimode fields - open quantum system

I read paper on open quantum system, that talk about non-Markovian process and memory effects. they described the system as a generic decoherence model of two qubits interacting with correlated ...
Yohay Halfon's user avatar
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Linearity of Lindblad equation in the Heisenberg picture

I am interested in solving the dual (adjoint) Lindblad master equation for a time-dependent operator $O(t)$ as follows \begin{equation} \dot{O}(t) = i[H, O(t)]+\sum_{\alpha\in I} L_\alpha ^\dagger O(t)...
GSLAM's user avatar
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Why does permanent magnet not exhibit macroscopic quantum effect?

Permanent magnets are a result of quantum mechanics, i.e. quantum spin of electrons inside the magnet aligning. Quantum spin follows the uncertainty principle. If I measure the spin orientation first ...
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Stationary state of Lindblad equation

Is it true that a generic operator that is annihilated by the Lindblad superoperator (with both Hamiltonian and dissipative parts of the dynamics) has to be annihilated separately by both the ...
lgotta's user avatar
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On properties of open quantum dynamics and Lindbladians

It is well known that the open quantum dynamics is governed by the Lindblad master equation $$\partial_t{\rho}=\mathbb{L}(\rho)=-\frac{i}{\hbar}[H, \rho]+\sum_i \gamma_i\left(L_i \rho L_i^{\dagger}-\...
ironmanaudi's user avatar
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Lindblad evolution as continuum limit of a discrete process coupling system and environment

I have trouble understanding the derivation of the Lindblad evolution in terms of the time evolution under a Hamiltonian $H$ in a system-environment Hilbert space $H_S\otimes H_E$, where we trace out ...
Andi Bauer's user avatar
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1 answer
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Contractivity of the Lindblad Generator Adjoint

In the context of the Lindblad equation in the Heisenberg picture, the adjoint of the Lindblad generator, denoted as $\mathcal{L}^\dagger$, is known to be non-contractive in different cases. I would ...
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How to calculate $Tr_{E} \underbrace{[\rho^{bath} \otimes \rho^{bath}......\otimes \rho^{bath}]}_{N \ times}$ if I know $Tr_{E} [\rho^{bath}]$?

One can directly jump to the question and skip the first two paragraphs (motivation for the question) Consider a system in a thermal gas of $N$ particles. If I want to study the reduced dynamics of ...
Lost's user avatar
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Schmidt decomposition of density matrix

For a bipartite system: $\mathcal{H}=\mathcal{H}_{a}\otimes\mathcal{H}_{b}$ described by a density operator $\hat{\rho}_{ab}$, I can promote it to a vector in the Liouville space, $|\hat{\rho}_{ab}\...
Oscarcillo's user avatar
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How to construct the jump operator in the Lindblad Equation for a 2-qubit system?

I am working on a project for my degree to model a CNOT gate and I'm trying to do this with the Lindblad equation. $$ \dot{\rho} = -\dfrac{i}{\hbar} [H, \rho] + \sum\limits_i \gamma _i (L_i \rho L _i ^...
rb101's user avatar
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Implementation of Hamiltonian coupling to a bath

I want to study a system coupled to a bath, however I do not fully understand how to implement/think of the Hamiltonian. For simplicity say the bath is given by a spin chain (PBC), e.g. Ising-like $$...
qising's user avatar
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2 answers
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Finding error in Choi matrix calculation which suggests a CP map is not CP

The question Consider the following linear, trace preserving quantum map over $d \times d$ quantum states $\sigma$, $$\Phi(\sigma) = \Pi_R \sigma \Pi_R + (1 - \text{Tr}(\Pi_R \sigma)) \frac{\Pi_R}{R}$$...
nightshade's user avatar
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"Jump" operators from Lindblad equation where the external system is measurements

How do we derive the "jump operators" for the Lindblad equation if the external system is measurements? For example in this article for the Bose Hubbard system the Lindblad operators ...
poliroika's user avatar
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Bloch vector, maaster equation, and Bloch equation [closed]

I was confused about a derivation of Bloch equation in Breuer and Petruccione's The theory of Open Quantum Systems. Can someone gives some hints on derivation from Eq. 3.219 to Eq. 3.226? Specific ...
Wenhao Xu's user avatar
1 vote
1 answer
100 views

Bound on Lindblad Jump Operators

I am trying to understand the jump operators in the Lindblad equation. Specifically, if there is any condition of boundedness we need to impose on them. I ask this because, as was pointed out in this ...
tumm's user avatar
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References about advanced quantum mechanics

I have already studied quantum mechanics (Sakurai and Bransden Atomic/Molecular physics ) and all the relevant quantum field theory (Weinberg I + II, Schwartz and Birrell-Davies). I'm searching for ...
2 votes
1 answer
185 views

Harmonic Oscillators: Expectation value of the exponential of ladder operators

I am working with a spin-boson model. To figure out how the off-diagonal elements of the reduced density matrix for the system evolve, I need to figure out $\langle e^C\rangle$ where $C= c_{1}a+c_2a^{\...
Sal_99's user avatar
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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 ...
QuestionTheAnswer's user avatar
3 votes
1 answer
463 views

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, ...
slithy_tove's user avatar
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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 ...
EE18's user avatar
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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 ...
Anindita Sarkar's user avatar
6 votes
1 answer
385 views

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 = \...
FriendlyLagrangian's user avatar
3 votes
1 answer
213 views

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 ...
D.C's user avatar
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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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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 ...
userflux9674's user avatar
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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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4 votes
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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{...
Refik Mansuroglu's user avatar
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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)...
Turbotanten's user avatar
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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 ...
Prox's user avatar
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2 answers
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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 ...
Adrien Amour's user avatar
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2 answers
131 views

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 ...
Adrien Amour's user avatar
2 votes
2 answers
94 views

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 ...
Adrien Amour's user avatar
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165 views

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 ...
Jon Megan's user avatar
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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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