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I am working on an open system and I would like to use the Lindblad master equation but also I would like to add noise to it. If is possible.

All the books and papers I did read about tells me that in order to add noise you have to use the Quantum Langevian equation and derive the master equation from there. Which is, of course, different from the Lindblad master equation.

My question is: can I add noise to the Lindbland master equation? If the answer is positive can someone please point me to where to find such information?

Thank you

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  • $\begingroup$ Yes, what you are asking for is usually called a (quantum) stochastic master equation. It appears in the context of measurement theory, specifically that of homodyne or heterodyne measurements. $\endgroup$ – Mark Mitchison Sep 29 '17 at 10:00
  • $\begingroup$ Thank you very much. If is not much to ask, can you point me to any major paper or book on the matter? $\endgroup$ – Lonodon243 Sep 29 '17 at 19:54
  • $\begingroup$ When you do say "quantum stochastic master equation" you are referring to the Belavkin equation or to some other master equation? $\endgroup$ – Lonodon243 Sep 29 '17 at 20:17
  • $\begingroup$ Yeah, the Belavkin equation is one example. The book by Wiseman and Milburn on quantum measurement is an excellent reference for these topics. $\endgroup$ – Mark Mitchison Sep 30 '17 at 0:06
  • $\begingroup$ If you don't mind me asking, what work are you doing? And are you adding white-noise into your system or something? I recently got into quantum machine learning and adding noise into the quantum system is something I am interested in as well. $\endgroup$ – user209663 Sep 27 '18 at 19:14
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It depend on the noise type that you want to use, for white noise in many case you can use Lindblad equation and a proper super-operator to implement the noise. Look for example at this Prof.Dr. Pelenio's article:

http://iopscience.iop.org/article/10.1088/1367-2630/10/11/113019/meta

You can get the article from their research-gate profile for free.

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