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

This paper solves the newly constructed nonlinear master equation dρ/dt=κ[2f (N) aρ (1/f (N-1))a+-a+aρ-ρa+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 f (N)=1/(N+1)～(1/2).     

Evolution of a two-mode squeezed vacuum in the amplitude dissipative channel

For the first time we derive the dissipating result of an initial two-mode squeezed pure vacuum state passing through a two-mode amplitude dissipative channel described by the direct product of two independent single-mode master equations. Although these two master equations do not mix the two modes (there is no coupling between them), since the two-mode squeezed state is simultaneously an entangled state, the final state which emerges from passing this channel is a two-mode mixed density operator. The compact expression of the outcoming state is obtained, which manifestly shows that as time evolves, the squeezing effect decreases.     

A generalized tripartite scheme for splitting an arbitrary 2-qubit state with three 2-qubit partially entangled states and the Kraus measurement

We put forward a generalized tripartite scheme for splitting an arbitrary 2-qubit pure state with three 2-qubit non-maximally en-tangled states as quantum channels.The scheme for the first time incorporates the Kraus measurement into quantum information splitting scheme.In contrast to the similar scheme using the same quantum channels and the ancilla-entangled measurement,our scheme is superior in terms of operation and complexity,success probability,resource consumption and effciency.     

A new optical field state as an output of diffusion channel when the input being number state

By analyzing theoretical scheme of quantum controlling through photon addition,we propose a new optical field whose density operator asρ=λ(1-λ)l:Ll(-λ2aa/1-λ)e-λaa:(here::denotes normal ordering symbol),which is named Laguerre-polynomialweighted chaotic state.We show that such state is the solution to the master equation d/dtρ=-κ(aaρ+ρaa-aρa-aρa),describing a diffusion channel,with the initial number state|l l|,andλ=1/(1+κt).This new state is characteristic of possessing photon number l+κt at time t,so the photon number by adjusting the diffusion parameterκcan be controlled.This master equation is solved using the summation method within ordered product of operators and the entangled state representation.The physical difference between the diffusion and the amplitude damping is noted.     

Solving Master Equation for Two-Mode Density Matrices by Virtue of Thermal Entangled State Representation

We extend the approach of solving master equations for density matrices byprojecting it onto the thermal entangled state representation (Hong-Yi Fanand Jun-Hua Chen, J. Phys. A35 (2002) 6873) to two-mode case. In thisapproach the two-photon master equations can be directly and convenientlyconverted into c-number partial differential equations. As an example, wesolve the typical master equation for two-photon process in some limitingcases.     

Dissipation of a two-mode squeezed vacuum state in the single-mode amplitude damping channel

We explore how a two-mode squeezed vacuum state sechθ e^{a+b+ tanh θ} |00> evolves when it undergoes a singlemode amplitude dissipative channel with rate of decay κ. We find that in this process not only the squeezing parameter decreases, tanh θ → e^-κt tanh θ, but also the second-mode vacuum state evolves into a chaotic state exp{b⁺bln[1 - e^-2κt tanh² θ]}. The outcome state is no more a pure state, but an entangled mixed state.     

New approach for analysing master equations of generalized phase diffusion models in the entangled state representation

By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective. This method can also be applied to solve other master equations.     

Dynamics of Quantum Entanglement in Reservoir with Memory Effects

The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects.The completely positive reduced dynamical map can be constructed in the Kraus representation.Quantum entanglement decays more slowly in the non-Markovian environment.The decoherence time for quantum entanglement can be markedly increased with the change of the memory kernel.It is found out that the entanglement sudden death between quantum systems and entanglement sudden birth between the system and reservoir occur at different instants.     

量子力学纠缠态表象

扼要介绍了笔者近期提出的纠缠态表象的性质与应用。     

New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation

By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial （TVHP）. By them and the technique of integration within an ordered product （IWOP） of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.     

Time evolution of distribution functions in dissipative environments

By introducing the thermal entangled state representation,we investigate the time evolution of distribution functions in the dissipative channels by bridging the relation between the initial distribution function and the any time distribution function.We find that most of them are expressed as such integrations over the Laguerre-Gaussian function.Furthermore,as applications,we derive the time evolution of photon-counting distribution by bridging the relation between the initial distribution function and the any time photon-counting distribution,and the time evolution of Rfunction characteristic of nonclassicality depth.     

Some New Properties of Wigner Function Studied in Entangled State Representation

Based on the Wigner operator in the entangled state representation we study some new important properties of Wigner function for bipartite entangled systems, such as size of an entangled state, upper bound of Wigner functions, etc. These discussions demonstrate the beauty and elegance of the entangled state representation.     

Efficient scheme for teleportation of an unknown N-atom state via a two-atom entangled state without the Bell-state measurement in cavity QED

We propose a scheme for teleportation of an unknown N-atom state using a two-atom entangled state within a cavity QED and show the feasibility in experiment. Our scheme does not involve the Bell-state measurement and is insensitive to the cavity decay, which is important from the experimental point of view. Another feature of the scheme is that teleporting a N-atom state just requires a small amount of entanglement （i,e. a two-atom entangled state） and less classical bits （two bits）.     

Quantum properties of the binomial state field interacting with a two-level atom

By the method of coherent-state orthogonalization expansion,the atomic inversion and the anti-bunching effect in a two-level atomic system interacting with binomial state field are studied under the Jaynes-Cummings model without rotating wave approximation.The influence of the parameter and the detuning on the anti-bunching effect are discussed,and the anti-bunching effect is also discussed under the conditions of strong coupling.Our studies show that the second order coherence degrees are quite different b...     

The squeezing entangled state of two particles with unequal mass

For two unequal-mass particles,we construct the entangled state representation and then derive the corresponding squeezing operator.This squeezing operator has a natural realization in the entangled state representation,which exhibits the intrinsic relation between squeezing and quantum entanglement.This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings.The maximum squeezing occurs when the two particles possess equal mass.When the two particles’ mass difference becomes large,the component of the two single-mode squeezings becomes dominant.     

Decoherence of photon-subtracted squeezed vacuum state in dissipative channel

This paper investigates the decoherence of photo-subtracted squeezed vacuum state (PSSVS) in dissipative channel by describing its statistical properties with time evolution such as Wigner function,Husimi function,and tomogram.It first calculates the normalization factor of PSSVS related to Legendre polynomial.After deriving the normally ordered density operator of PSSVS in dissipative channel,one obtains the explicit analytical expressions of time evolution of PSSVS’s statistical distribution function.It finds that these statistical distributions loss their non-Gaussian nature and become Gaussian at last in the dissipative environment as expected.     

Probabilistic teleportation of an unknown N-atom state using a two-atom nonmaximally entangled state in cavity QED

We present a scheme for realizing probabilistic teleportation of an unknown N-atom state via cavity QED. This scheme requires only a nonmaximally entangled pair to be used as a quantum channel, so the requirement of entanglement is reduced. In addition, our scheme does not involve the Bell-state measurement and is insensitive to the cavity decay, which is important from the experimental point of view. If the quantum channel is a two-atom maximally entangled state, teleportation of an unknown N-atom state can be realized by a simpler scheme via cavity QED.     

function for the squeezed atomic coherent state in entangled state representation and some of its applications

Based on the Einstein, Podolsky, and Rosen (EPR) entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state (SACS), which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.     

在量子光学框架中研究魏格纳-维利分布

我们在量子光学框架中研究光信号的魏格纳-维利分布,指出利用魏格纳算符和纠缠魏格纳算符的显示正规乘积形式以及压缩算符的纠缠态表象,这方面的研究就可做到数学上简明和物理上有吸引力.