Time Evolution of Husimi Function for Photon-Added Squeezed Vacuum State in Dissipative Channel

In this paper, we determine the normalization factor of photo-added squeezed vacuum state (PASVS) as a Legendre polynomial of the squeezing parameter by virtue of principle of mathematical induction, and derive the normally ordered density operator of PASVS in dissipative channel. In addition, we also give the explicit analytical expression of Husimi function in dissipative channel and study its behavior with evolution time graphically.     

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

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^-2kt, 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.     

激发相干态在耗散量子通道中Husimi函数的演化

基于有序算符内的积分技术和量子力学相干态表象,本文研究了激发相干态在耗散量子通道中的Husimi函数的演化情况,首次推导了Husimi函数在耗散量子通道中的解析表达式,并通过绘制图形讨论了各种参数对Husimi函数的影响。     

Entanglement Involved in Time Evolution of Two-Mode Squeezed State in Single-Mode Diffusion Channel

We derive the evolution law of an initial two-mode squeezed vacuum state \( \text {sech}^{2}\lambda e^{a^{\dag }b^{\dagger }\tanh \lambda }\left \vert 00\right \rangle \left \langle 00\right \vert e^{ab\tanh \lambda }\) (a pure state) passing through an a-mode diffusion channel described by the master equation

$$\frac{d\rho \left( t\right) }{dt}=-\kappa \left[ a^{\dagger}a\rho \left( t\right) -a^{\dagger}\rho \left( t\right) a-a\rho \left( t\right) a^{\dagger}+\rho \left( t\right) aa^{\dagger}\right] , $$

since the two-mode squeezed state is simultaneously an entangled state, the final state which emerges from this channel is a two-mode mixed state. Performing partial trace over the b-mode of ρ(t) yields a new chaotic field, \(\rho _{a}\left (t\right ) =\frac {\text {sech}^{2}\lambda }{1+\kappa t \text {sech}^{2}\lambda }:\exp \left [ \frac {- \text {sech}^{2}\lambda }{1+\kappa t\text {sech}^{2}\lambda }a^{\dagger }a \right ] :,\) which exhibits higher temperature and more photon numbers, showing the diffusion effect. Besides, measuring a-mode of ρ(t) to find n photons will result in the collapse of the two-mode system to a new Laguerre polynomial-weighted chaotic state in b-mode, which also exhibits entanglement.

     

Amplitude Nth-power Squeezings in a Normal Squeezed Vacuum State

1.IntroductionSqueezedstates0fradiati0nficlds[1avebeenstudicdc0nsiderablyinrecentyears.Besidesthen0rma1lsqueezing,itisals0possibletodefinehigl1pr-ordersqueezings.HongandMan-de1[1Jdefinedthe'2Nth-ordersqueezing,andHillery[2]intr0ducedtheamp1itudesquared.squeezing.Morerecently,Zhangclal.[3JsuggcstedtheamplitudeNth-p0wersqueezingwhichincludosthenorma1squeezingandtheamplitude-squaredsqueezingassPecialcases.Allthese:higher-ordersqueezingshavebeensho`\)ntobeindependentnonclassica1features0f.radi…     

Dissipation of Two-Mode Squeezed State in Two Independent Amplitude Dissipative Channels

We examine the dissipative result of a pure two-mode squeezed state passing through two independent amplitude dissipative channels described by the direct product of two independent single-mode master equations. Although these two master equations do not mix the two modes (no coupling between them), but since the two-mode squeezed state is simultaneously an entangled state, the output state emerging from the two channels is a two-mode density operator (mixed state). The exact and compact expression of the outcoming state is obtained, which manifently shows that as time evolves the squeezing effect and photon number decreases.     

Generalized Thermo Vacuum State Derived by the Partial Trace Method

By virtue of the technique of integration within an ordered product of operators, we present a new approach for deriving the generalized thermo vacuum state which is simpler in form than that obtained from the Takahashi -Umezawa method, using this new approach, the thermo field dynamics can be developed. Applications of the new state are discussed.     

Dissipative Evolution of the Qubit State in the Tomographic-Probability Representation

We consider the evolution of qubit states for the Demkov problem in the presence of dephasing processes in the spin tomographic-probability representation. We present an explicit solution of the spin tomogram in terms of the ₁ F ₂ hypergeometric function. We calculate the tomographic Shannon and q entropies through the solution of the master equation in the form of tomographic-probability distribution of the qubit states obtained.     

Thermo Vacuum State for Describing the Density Operator of Photon-subtracted Squeezed Chaotic Light

For the density operator describing s?photon-subtracted squeezed chaotic light (PSSCL) we search for its thermo vacuum state (a pure state) in the real-fictitious space. We find that it reduces to a thermo vacuum state of squeezed chaotic light when s = 0, and to a thermo vacuum state of the optical negative binomial field when no squeezing. The new thermo vacuum state simplifies calculating photon number average, quantum fluctuation and Mandel’s Q parameter of PSSCL. Using the method of integration within ordered product (IWOP) of operators we also derive the normalization coefficient and explicitly analytical expressions of Wigner function for PSSCL.     

Evolution Law of the Optical Field of Degenerate Parametric Amplifier in Dissipative Channel

We explore the time-evolution law of the optical field of degenerate parametric amplifier (DPA) in dissipative channel. It turns out that its density operator at initial time ρ ₀ = A exp(E ^? a ^?2) exp(a ^? alnλ) exp(E a ²) evolves into \(\rho (t)= \frac {A}{\lambda ^{\prime }}\) \(\exp \left (\frac {E^{\ast }e^{-2\kappa t}a^{\dag 2}}{ \lambda ^{\prime 2}}\right )\exp \left \{a^{\dag }a\ln \frac {[\lambda -(\lambda ^{2}-4|E|^{2})T]e^{-2\kappa t}}{\lambda ^{\prime 2}}\right \} \exp \left (\frac { Ee^{-2\kappa t}a^{2}}{\lambda ^{\prime 2}}\right ),\) where κ is the damping constant of the channel, T = 1 ? e ^?2κt , and \(\lambda ^{\prime }\equiv \sqrt {(1-\lambda T)^{2}-4|E|^{2}T^{2}}.\) We employ the method of integration (or summation) within an ordered (normally ordered or antinormally ordered) of operators to overcome the obstacles in the process of calculation.     

Stochastic Resonance in Linear Region of a Single-Mode Laser： Effects of Amplitude Modulation of Signal

A single-mode laser noise model driven by quadratic colored pump noise and amplitude modulation signal is proposed. The real and imaginary parts of the pump noise are assumed to be cross-correlation. The effect of cross-correlation of noise and amplitude modulation of signal on laser statistical properties is studied by using the linearized approximation. The analytic expression of signal-to-noise ratio (SNR) is calculated. It is found that the phenomena of stochastic resonance (SR) respectively exist in the curves of the SNR versus the noise cross-correlation coefficient λ and the SNR versus the pump parameter a, as well as the SNR versus the signal frequency ω in our model. It is shown that there are three different typies of SR in the model: the conventional form of SR, the SR in the broad sense, and the bona fide SR.     

Entanglement-Assisted Classical Capacity of a Generalized Amplitude Damping Channel

The entanglement-assisted capacity of a generalized amplitude damping channel is investigated by using the properties of partial symmetry and concavity of mutual information. The numerical and analytical results of the entanglement-assisted capacity are obtained under certain conditions. It is shown that the entanglement-assisted capacity depends on the channel parameters representing the ambient temperature and dissipation, and the prior entanglement between sender and receiver can approximately double the classical capacity of the generalized amplitude damping channel.     

The Evolution Feature of Chirp-Dark Soliton in Single-Mode Fiber

The evolution feature of the injected initial-chirp tanh-dark soliton in single-mode fiber is studied in this paper. We analyze the evolution of amplitude, pulse width, frequency chirp and center position shift of dark soliton along with the variation of propagation distance, primarily using Lagrange-Euler's formula and taking the high-order dispersion as perturbation. The results show that the amplitude and pulse width of chirp-dark soliton are all oscillating around a certain critical distance in ideal fiber (β = 0), and the high-order dispersion conduces to generate the asymptotic dark soliton.     

Initializing the Amplitude Distribution of a Quantum State

To date, quantum computational algorithms have operated on a superposition of all basis states of a quantum system. Typically, this is because it is assumed that some function f is known and implementable as a unitary evolution. However, what if only some points of the function f are known? It then becomes important to be able to encode only the knowledge that we have about f. This paper presents an algorithm that requires a polynomial number of elementary operations for initializing a quantum system to represent only the m known points of a function f.     

Stochastic Resonance in a Single-Mode Laser Driven by Quadratic Colored PumpNoise: Effects of Biased Amplitude Modulation Signal

A single-mode laser noise model driven by quadratic colored pump noise andbiased amplitude modulation signal is proposed. The analytic expression ofsignal-to-noise ratio is calculated by using a new linearized procedure. Itis found that there are three different typies of stochastic resonance inthe model: the conventional form of stochastic resonance, the stochasticresonance in the broad sense, and the bona fide SR.     

Fidelity of Quantum Teleportation for Single-Mode Squeezed State Light

The fidelity of quantum teleportation of a single-mode squeezed state of light is calculated based on the general theory of quantum-mechanical measurement in the Schrodinger picture. It is shown that the criterion for the nonclassical state teleportation is different from that for coherent state. F = 1/2 is no longer the rigorous boundary between classical and quantum teleportation for a squeezed state of light. When the quantum entanglement of an Einstein-Podolsky-Rosen （EPR） beam used for teleportation and the parameters of the system are given, the fidelity depends on the squeezing of the input squeezed state. The higher the squeezing is, the smaller the fidelity is, and the lower the classical limitation of fidelity is. The dependence of the optimum gain for teleporting a squeezed vacuum state upon the EPR entanglement is also calculated. The results obtained provide important references for designing experimental systems of teleporting a non-classical state and judging the quality of the teleported quantum state.