Completely positive reduced dynamics with non-Markovian initial states

Nazifkar, Samira; Sargolzahi, Iman

doi:10.47176/ijpr.22.4.61469

Completely positive reduced dynamics with non-Markovian initial states

Document Type : Original Article

Authors

Samira Nazifkar

Iman Sargolzahi

Department of Physics, University of Neyshabur, Neyshabur, Iran

https://doi.org/10.47176/ijpr.22.4.61469

Abstract

Consider an open quantum system S, interacting with its environment E, and also an ancillary Hilbert space R. The reduced dynamics of the system S is given by a completely positive map, if the set S={ρ_SE} , of possible initial states of the system-environment, can be written as a steered set from a tripartite Markov state Ʈ_RSE. In this paper, we call such steered states as Markovian states ρ_SE, and study a physical case, in which the reduced dynamics of the system can be completely positive, even when the initial states of the system-environment ρ_SE are non-Markovian.

Keywords

open quantum system

completely positive map

Markov state

20.1001.1.16826957.1401.22.4.19.5

Subjects

Theoretical

M A Nielsen and I L Chuang, “Quantum Computation and Quantum Information” Cambridge University Press, Cambridge (2000).
D A Lidar, arXiv:1902.00967 (2019).
A Rivas and S F Huelga, "Open Quantum Systems: An Introduction", Springer, Heidelberg (2011).
C A Rodríguez-Rosario, et al., J. Phys. A 41 (2008) 205301.
A Shabani and D A Lidar, Phys. Rev. Lett. 102 (2009) 100402; 116 (2016) 049901(E).
L Liu and D M Tong, Phys. Rev. A 90 (2014) 012305.
A Brodutch, et al., Phys. Rev. A 87 (2013) 042301.
F Buscemi, Phys. Rev. Lett. 113 (2014) 140502.
X M Lu, Phys. Rev. A 93 (2016) 042332.
I Sargolzahi and S Y Mirafzali, Open Syst. Info. Dyn. 25 (2018) 1850012.
I Sargolzahi and S Y Mirafzali, Phys. Rev. A 100 (2019) 042121.
D Salgado and J L Sanchez-Gomez, arXiv:quant-ph/0211164 (2002).
P Lambropoulos and D Petrosyan, “Fundamentals of Quantum optics and Quantum Information”و Springer, Berlin (2007).
P Hayden, et al., Commun. Math. Phys. 246 (2004) 359.
I Sargolzahi, J. Phys. A: Math. Theor. 51 (2018) 315301.
P Pechukas, Phys. Rev. Lett. 73 (1994) 1060.
J M Dominy, et al., Quant. Inf. Process. 15 (2016) 465.
I Sargolzahi, Iran. J. Phys. Res. 21, 3 (2021) 451(in Persian).
I Sargolzahi, Phys. Rev. A 102 (2020) 022208.
I Sargolzahi, Iran. J. Phys. Res. 20, 2 (2020) 267(in Persian).