Questions tagged [open-quantum-systems]

For questions about the effect of a quantum system's environment on the system of interest.

34 questions
9
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What kinds of objects are Liouvillian, Lindbladian, and Davies generator?

I have a rather basic question. I'm starting to read papers such as Chen–Brandao, Chen–Kastoryano–Brandao–Gilyen, and I'm having trouble parsing even what kind of objects a Liouvillian, Lindbladian, and Davies generator are. It seems that the Davies…
zjs
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6
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Show that if the Lindblad satisfy $\sum_\mu L_\mu L_\mu^\dagger=\sum_\mu L_\mu^\dagger L_\mu$ then the von Neumann entropy increases monotonically

How can we show that when the Lindblad operators satisfy the condition: $$\sum_{\mu}L_{\mu} L_{\mu}^{\dagger} = \sum_{\mu} L_{\mu}^{\dagger}L_{\mu},\tag{1}$$ the master equation evolution monotonically increases the von Neumann entropy. When…
6
votes
1 answer

What does it mean for a channel to be independent of the input state?

A 2007 paper shows how to construct quantum channels on finite-dimensional Hilbert spaces $$\sigma=\Phi(\rho)=\sum_i K_i \rho K_i^\dagger,\qquad \sum_i K_i^\dagger K_i=\mathbb{I}$$ for which $\Phi(\rho)=\sigma$ is independent of $\rho$. This seems…
5
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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…
5
votes
1 answer

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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5
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2 answers

What properties do Kraus operators of Markovian processes have?

It is well-known that the Kraus operator can describe more kinds of processes than master equations. For example, the master equation cannot describe non-markovian processes while the Kraus operator can, and all master equations can be translated…
narip
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5
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Only assuming the universe evolves according to a positive trace-preserving map, is there a proof that all subsystem evolution must be CPTP?

If we only assume that the wavefunction of the universe evolves according to $e^{-iHt}$, is there any proof that all subsystems of the universe (partial traces over parts of the universe) must evolve according to a completely positive,…
4
votes
1 answer

Why do quantum computation models based on open quantum systems receive so little attention?

In almost all research on (universal) quantum computation the common models assumed from the outset are either the quantum circuit model with unitary gates, the measurement-based one-way model or the adiabatic model - all of which are (polynomially)…
4
votes
1 answer

Plotting Bloch sphere in QuTiP

Is there anyone who reproduced the Bloch sphere given in the paper QuTiP: An open-source Python framework for the dynamics of open quantum systems by J. R. Johansson, P. D. Nation, Franco Nori? I am trying to reproduce the Figure 10: Bloch sphere…
4
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0 answers

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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4
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Is it overestimating noise in a QPU if we use infidelities and also quantum channel such as depolarising or amplitude damping?

I have mainly seen two ways of studying noise in quantum algorithm simulation. The first one is to suppose that your quantum gate can be implemented with a probability of success of $\mathcal{F}$ (being this the fidelity of the gate). If it is not…
q_man
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4
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1 answer

Deriving Bloch vector $dr$ from master equation

I am trying to derive the Bloch vector $dr$ for a measurement of a observable in an arbitrary direction $\theta$. For context this is the setup and derivation I have for continuous measurement along the $z$ axis. The equation of continuous…
3
votes
1 answer

General Master Equation with Decoherence Query

The following general master equation (from this paper 'Dynamical quantum correlations of Ising models on arbitrary lattice and their resilience to decoherence') describes the various types of decoherence relevant to trapped ions, Rydberg atoms and…
John Doe
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3
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1 answer

Finding a density matrix for a distribution of pure states

Let $\theta$ be a Gaussian variable with mean 0 and variance 1. Then for $t>0$, the variable $\theta \sqrt{t}$ is also Gaussian with mean $0$ and variance $t$. Let $|\psi_0\rangle$ be an arbitrary state on a Bloch sphere. Define $$|\psi(t)\rangle :=…
3
votes
1 answer

Do all Hermiticity-preserving maps generate completely positive maps?

I am confused about what kinds of maps are valid infinitesimal generators of completely positive maps. I know that any Markovian completely positive map can be written in the form $e^{t \mathcal{L}}$, where $\mathcal{L}$ is the Linbladian, a…
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