Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics B

Solving nonlinear master equation describing quantum damping by virtue of the entangled state representation

Hong-Yi Fan, Gang Ren, Liyun Hu, Nian-Quan Jiang

Published Nov 1, 2010• 9 citations
Publisher

Abstract

This paper solves the newly constructed nonlinear master equation dρ/d t = κ[2 f ( N ) a ρ (1/ f ( N − 1)) a † − a † a ρ−ρ a † a ], where f ( N ) is an operator-valued function of N = a † a , for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field (a mixed state) when

DOI
10.1088/1674-1056/19/11/114206

Related papers

Evolution of Number State to Density Operator of Binomial Distribution in the Amplitude Dissipative Channel

Fan Hong‐Yi, Gang Ren

We show that passing through the amplitude dissipative channel the initial pure number state density operator is evolved into the density operator of binomial distribution (a mixed state), and the binomial distribution parameter is just equal to e −2 kt , where k is the dissipative parameter of the channel. We solve the corresponding master equation to obtain the operator-sum representation of the density operator by virtue of the entangled state representation, which seems to be a convenient approach.

Chinese Physics Letters•May 1, 2010•10 citations

OPERATOR-SUM REPRESENTATION OF DENSITY OPERATORS AS SOLUTIONS TO MASTER EQUATIONS OBTAINED VIA THE ENTANGLED STATE APPROACH

Hong-Yi Fan, Liyun Hu

We solve various master equations to obtain density operators' infinite operator-sum representation via a new approach, i.e., by virtue of the thermo-entangled state representation that has a fictitious mode as a counterpart mode of the system mode. The corresponding Kraus operators from the point of view of quantum channel are derived, whose normalization conditions are proved. Miscellaneous characters possessed by different quantum channels, such as decoherence, phase diffusion, damping, and amplification, can be shown explicitly in the entangled state representation of the density operators. Squeezing transformation is applied to the density operator for decoherence to generate a master equation for describing the phase sensitive process. Partial trace method for deriving new density operators is also introduced. Throughout our discussion, the technique of integration within an ordered product (IWOP) of operators is fully used.

Modern Physics Letters B•Oct 10, 2008•111 citations

Density operator for describing driven damped harmonic oscillator in the diffusion-limited channel

Hong-Yi Fan, Qian-Fan Chen

In the present work, the Kraus-operator sum representation of the exact solution to the master equation describing a harmonic oscillator (driven by an external source) damping in the diffusion-limited channel is obtained by virtue of the thermo-entangled state representation and the technique of integration within an ordered product of operators. According to this solution, the initial coherent state will evolve into a displaced chaotic state that manifestly exhibits quantum decoherence.

Canadian Journal of Physics•Jan 23, 2014•2 citations

New Approach for Solving Master Equations in Quantum Optics and Quantum Statistics by Virtue of Thermo-Entangled State Representation

Fan Hong‐Yi, Liyun Hu

By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation ?|, which can arrange master equations of density operators ?(t) in quantum statistics as state-vector evolution equations due to the elegant properties of ?|. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of the decay constant ? we find that the matrix element of ?(t) at time t in ?| representation is proportional to that of the initial ?0 in the decayed entangled state ?e??t| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ? = ?(d2?/?)?|?D(?), which is different from all the previous known representations.

Communications in Theoretical Physics•Apr 1, 2009•21 citations

New approach to solving master equations of density operator for the Jaynes Cummings model with cavity damping

Seyed, Mahmoud, Ashrafi +3 more

By introducing thermo-entangled state representation |η>, which can map master equations of density operator in quantum statistics as state-vector evolution equations, and using dissipative interaction picture we solve the master equation of Jaynes–Cummings model with cavity damping. In addition we derive the Wigner function for density operator when the atom is initially in the up state |↑> and the cavity mode is in coherent state.

中国物理B：英文版•Jan 1, 2014•0 citations

New approach to solving master equations of density operator for the Jaynes Cummings model with cavity damping

Seyed Mahmoud Ashrafi, M. R. Bazrafkan

By introducing thermo-entangled state representation |η〉, which can map master equations of density operator in quantum statistics as state-vector evolution equations, and using "dissipative interaction picture" we solve the master equation of Jaynes—Cummings model with cavity damping. In addition we derive the Wigner function for density operator when the atom is initially in the up state |↑〉 and the cavity mode is in coherent state.

Chinese Physics B•Sep 1, 2014•9 citations
This paper solves the newly constructed nonlinear master equation dρ/d t = κ[2 f ( N ) a ρ (1/ f ( N − 1)) a † − a † a ρ−ρ a † a ], where f ( N ) is an operator-valued function of N = a † a , for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field (a mixed state) when
We show that passing through the amplitude dissipative channel the initial pure number state density operator is evolved into the density operator of binomial distribution (a mixed state), and the binomial distribution parameter is just equal to e −2 kt , where k is the dissipative parameter of the channel. We solve the corresponding master equation to obtain the operator-sum representation of the density operator by virtue of the entangled state representation, which seems to be a convenient approach.
We solve various master equations to obtain density operators' infinite operator-sum representation via a new approach, i.e., by virtue of the thermo-entangled state representation that has a fictitious mode as a counterpart mode of the system mode. The corresponding Kraus operators from the point of view of quantum channel are derived, whose normalization conditions are proved. Miscellaneous characters possessed by different quantum channels, such as decoherence, phase diffusion, damping, and amplification, can be shown explicitly in the entangled state representation of the density operators. Squeezing transformation is applied to the density operator for decoherence to generate a master equation for describing the phase sensitive process. Partial trace method for deriving new density operators is also introduced. Throughout our discussion, the technique of integration within an ordered product (IWOP) of operators is fully used.
By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation ?|, which can arrange master equations of density operators ?(t) in quantum statistics as state-vector evolution equations due to the elegant properties of ?|. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of the decay constant ? we find that the matrix element of ?(t) at time t in ?| representation is proportional to that of the initial ?0 in the decayed entangled state ?e??t| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ? = ?(d2?/?)?|?D(?), which is different from all the previous known representations.