Linear reduced dynamics

Sargolzahi, I

doi:10.47176/ijpr.20.2.31025

Linear reduced dynamics

Document Type : Original Article

Author

I Sargolzahi

1. Department of Physics, University of Neyshabur, Neyshabur, Iran 2. Research Department of Astronomy & Cosmology, University of Neyshabur, Neyshabur, Iran

https://doi.org/10.47176/ijpr.20.2.31025

Abstract

Consider an open quantum, system interacting with its environment. Whether the reduced dynamics of the system can be given by a linear map or not is an important question in the theory of open quantum systems. Dominy, Shabani and Lidar have proposed a general framework for linear Hermitian reduced dynamics. In addition, it has been shown that their framework is, in fact, the most general one: The reduced dynamics of the system is linear if and only if it can be formulated within the Dominy-Shabani-Lidar framework. This result has been given in a rather abstract way. Here, we want to give another proof for it, in a more illustrative manner.

Keywords

open quantum systems

Hermitian maps

linear maps

M A Nielsen and I L Chuang, “Quantum Computation and Quantum Information”, Cambridge University Press, Cambridge (2000).

2. J M Dominy, A Shabani, and D A. Lidar, Quant. Inf. Process. 15 (2016) 465.

3. P Stelmachovic and V Buzek, Phys. Rev. A 64 (2001) 062106.

4. K M F Romero, P Talkner, and P Hanggi, Phys. Rev. A 69 (2004) 052109.

5. I Sargolzahi and S Y Mirafzali, Open Syst. Info. Dyn. 25 (2018) 1850012.

6. I Sargolzahi, Phys. Rev. A 102 (2020) 022208.

7. I Sargolzahi, Generalizing the Framework of Dominy-Shabani-Lidar for the Reduced Dynamics (unpublished).

8. E Brüning, H Mäkelä, A Messina, and F Petruccione, J. Mod. Opt. 59 (2012) 1.