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

We explore how a two-mode squeezed vacuum state sechθeab tanh θ[00） evolves when it undergoes a single- mode amplitude dissipative channel with rate of decay k. We find that in this process not only the squeezing parameter decreases, tanhθ → e-kt tanh θ, but also the second-mode vacuum state evolves into a chaotic state exp{bbln[（1 - e-2kt） tanh2 θ]}. The outcome state is no more a pure state, but an entangled mixed state.

Nonlinear two-mode squeezing obtained by analysing two-mode exponential quadrature operators in entangled state representation

By analysing the properties of two-mode quadratures in an entangled state representation （ESR） we derive from ESR some complicated exponential quadrature operators for nonlinear two-mode squeezing, which directly leads to wave function of the nonlinear squeezed state in ESR.

Coordinate-Dependent One- and Two-Mode Squeezing Transformation and the Corresponding Squeezed States

We introduce the coordinate-dependent one-and two-mode squeezing transformations and discuss theproperties of the corresponding one-and two-mode squeezed states.We show that the coordinate-dependent one-and two-mode squeezing transformations can be constructed by the combination of two transformations,a coordinate-dependentdisplacement followed by the standard squeezed transformation.Such a decomposition turns a nonlinear problem intoa linear one because all the calculations involving the nonlinear one- and two-mode squeezed transformation have beenshown to be able to reduce to those only concerning the standard one- and two-mode squeezed states.

Entanglement Transfer from Two-Mode Squeezed Vacuum State Field to Two Spatially Separated Atoms in Two-Photon Processes

我们在二光子的过程从二模式的挤压的真空状态地在纠纷转移上调查空移动的影响到二个空间地分开的原子。我们的结果证明空移动在如此的纠纷转移起一个重要作用。我们发现当空移动参数 r 是小的时，在二个原子之间的纠纷的度与首先增加压榨的参数 ξ 增加，并且在完成它的最大的价值以后，纠纷的度将与增加 &#958 减少到零；当时为大 r， E 将与增加 ξ 增加。

Some Properties of Two-mode Displaced Excited Squeezed Vacuum States

In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are investigated.Using the entangled state representation and Weyl ordering formof the Wigner operator,the Wigner functions of TDESVS are obtained and the variations of Wigner functions withthe parameters m,n and r are investigated.Besides,two marginal distributions of Wigner functions of TDESVS areobtained,which exhibit some entangled properties of the two-particle's system in TDESVS.

Two-Mode Excited Squeezed Vacuum State and Its Properties

在这篇论文，二模式的激动的挤压的真空状态(TESVS ) 被使用统计方法学习。由计算 TESVS 的正规化， Jacobi 多项式和一些新身份的一种新形式被获得。TESVS 的光子数字分发被给，它是 Jacobi 多项式的一种简单形式。用 Wigner 操作员的纠缠的州的表示， TESVS 的 Wigner 功能是 obtainded 和有参数 m， n，和 r 的 Wigner 功能的变化被讨论。这里，从阶段空间观点， TESVS 能很好被解释并且描述。

Quantum-enhanced optical precision measurement assisted by low-frequency squeezed vacuum states

Stable low-frequency squeezed vacuum states at a wavelength of 1550 nm were generated.By controlling the squeezing angle of the squeezed vacuum states,two types of low-frequency quadrature-phase squeezed vacuum states and quadrature-amplitude squeezed vacuum states were obtained using one setup respectively.A quantum-enhanced fiber Mach–Zehnder interferometer(FMZI)was demonstrated for low-frequency phase measurement using the generated quadrature-phase squeezed vacuum states that were injected.When phase modulation was measured with the quantumenhanced FMZI,there were above 3 dB quantum improvements beyond the shot-noise limit(SNL)from 40 kHz to 200 kHz,and 2.3 dB quantum improvement beyond the SNL at 20 kHz was obtained.The generated quadrature-amplitude squeezed vacuum state was applied to perform low-frequency amplitude modulation measurement for sensitivity beyond the SNL based on optical fiber construction.There were about 2 dB quantum improvements beyond the SNL from 60 kHz to 200 kHz.The current scheme proves that quantum-enhanced fiber-based sensors are feasible and have potential applications in high-precision measurements based on fiber,particularly in the low-frequency range.

Security of quantum key distribution using two-mode squeezed states against optimal beam splitter attack

For the beam splitter attack strategy against quantum key distribution using two-mode squeezed states, the analytical expression of the optimal beam splitter parameter is provided in this paper by applying the Shannon information theory. The theoretical secret information rate after error correction and privacy amplification is given in terms of the squeezed parameter and channel parameters. The results show that the two-mode squeezed state quantum key distribution is secure against an optimal beam splitter attack.

New formulas for normalizing photon-added(-subtracted) two-mode squeezed thermal states

For the first time,we derive the compact forms of normalization factors for photon-added（-subtracted） two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of operators（IWOP） technique.It is found that these two factors are related to the Jacobi polynomials.In addition,some new relationships for Jacobi polynomials are presented.

Construction of Laguerre polynomial's photon-added squeezing vacuum state and its quantum properties

Laguerre polynomial's photon-added squeezing vacuum state is constructed by operation of Laguerre polynomial's photon-added operator on squeezing vacuum state. By making use of the technique of integration within an ordered product of operators, we derive the normalization coefficient and the calculation expression of (a^1a^+). Its statistical properties, such as squeezing, the anti-bunching effect, the sub-Poissonian distribution property, the negativity of Wigner function, etc., are investigated. The influences of the squeezing parameter on quantum properties are discussed. Numerical results show that,firstly, the squeezing effect of the 1-order Laguerre polynomial's photon-added operator exciting squeezing vacuum state is strengthened, but its anti-bunching effect and sub-Poissonian statistical property are weakened with increasing squeezing parameter;secondly, its squeezing effect is similar to that of squeezing vacuum state, but its anti-bunching effect and subPoissonian distribution property are stronger than that of squeezing vacuum state. These results show that the operation of Laguerre polynomial's photon-added operator on squeezing vacuum state can enhance its non-classical properties.

Is the Cosmological Constant, a “Vacuum” Field? We Explore This by Squeezing Early Universe “Coherent-Semi Classical States”, and Compare This to Energy from the Early Universe Heisenberg Uncertainty Principle

Our question delves into the nature of early universe vacuum fields, and if this initial vacuum field corresponds to a configuration of early universe space-time at the start of inflation. The answer as to this came out due to wanting to know if a cosmological constant, as given in the Einstein field equations is commensurate with the byproduct of squeezed states. We compare our answer, with the influx of energy as given by a modified Heinsenberg uncertainty principle, at the start of the inflationary era. The so called influx of energy is tied into the squeezed state phenomena as written up in the onset of this article. The impetus to writing this document came from Dr. Karim, in an e mail which the author relates to, in the introduction. Our claim is that the smallness of is what is driving the existence of the squeezed states.

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.

Statistical properties of coherent photon-subtracted two-mode squeezed vacuum and its application in quantum teleportation

We introduce a kind of non-Gaussian entangled state, which can be obtained by operating a non-local coherent photon-subtraction operation on a two-mode squeezed vacuum. It is found that its normalization factor is only related to the Legendre polynomials, which is a compact expression. Its statistical properties are discussed by the negative region Wigner function with the analytical expression. As an application, the quantum teleportation for coherent states is considered by using the non-Gaussian state as an entangled channel. It is found that the teleportation fidelity can be enhanced by this non-Gaussian operation.

Single-mode quadrature-amplitude measurement for generalized two-mode squeezed states studied by virtue of the entangled state representation

The result of one-mode quadrature-amplitude measurement for some generalized two-mode squeezed states has been studied by virtue of the entangled state representation of the corresponding two-mode squeezing operators. We find that the remaining fleld-mode simultaneously collapses to the single-mode squeezed state with more stronger squeezing. The measurement result caused by a single-mode squeezed state projector is also calculated, which indicates quantum entanglement in squeezing.

Two-mode squeezed state of nanomechanical resonators

In this paper, we introduce a flexible model for the control and measurement of NAMRs （nanomechanical resonators）. We obtain the free Hamiltonian of the dcSQUID （direct current superconducting quantum interference device） and the interaction Hamiltonian between these two NAMRs and the dc-SQUID by introducing the annihilation and creation operators under the rotating wave approximation. We can treat the mode of the dc-SQUID as a classical field. In the Heisenberg picture, the generation of two-mode squeezed states of two nanomechanical resonators is shown by their collective coordinate and momentum operators.

The q-analogues of two-mode squeezed states constructed by virtue of the IWOP technique

The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product （IWOP） of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state S＇s（τ） │00） are investigated. It is found that, in different ranges of the squeezed parameter τ, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.

Quantum metrology with two-mode squeezed thermal state: Parity detection and phase sensitivity

Based on the Wigner-function method, we investigate the parity detection and phase sensitivity in a Mach–Zehnder interferometer(MZI) with two-mode squeezed thermal state(TMSTS). Using the classical transformation relation of the MZI, we derive the input–output Wigner functions and then obtain the explicit expressions of parity and phase sensitivity.The results from the numerical calculation show that supersensitivity can be reached only if the input TMSTS have a large number photons.

Photon statistical properties of photon-added two-mode squeezed coherent states

We investigate photon statistical properties of the multiple-photon-added two-mode squeezed coherent states （PA- TMSCS）. We find that the photon statistical properties are sensitive to the compound phase involved in the TMSCS. Our numerical analyses show that the photon addition can enhance the cross-correlation and anti-bunching effects of the PA- TMSCS. Compared with that of the TMSCS, the photon number distribution of the PA-TMSCS is modulated by a factor that is a monotonically increasing function of the numbers of adding photons to each mode; further, that the photon addition essentially shifts the photon number distribution.

Single-mode photon number measurement for the squeezed two-mode number state

Based on the fact that a two-mode squeezed number state is a two-variable Hermite polynomial excitation of the two-mode squeezed vacuum state, the result of one-mode l-photon measurement for the two-mode squeezed number state S2｜m, n） is discussed. It is found that a remaining field-mode simultaneously collapses into a number state ｜n - m＋l｜ with the coefficient being a Jacobi polynomial of n, m and l, which manifestly exhibits the entanglement between the two modes, i.e. it depends on the number-difference between the two modes. The second mode collapses into an excited coherent state when the first mode is measured as a coherent state.

Photon number cumulant expansion and generating function for photon added-and subtracted-two-mode squeezed states

For the first time, we derive the photon number cumulant for two-mode squeezed state and show that its cumulant expansion leads to normalization of two-mode photon subtracted-squeezed states and photon added- squeezed states. We show that the normalization is related to Jacobi polynomial, so the cumulant expansion in turn represents the new generating function of Jacobi polynomial.