Entangling two single-mode Gaussian states by use of a beam splitter

Considering two light beams which are in general single-mode Gaussian states and incident on input ports of an ideal beam splitter, respectively, this paper investigates how separability and entanglement of the output lights depend on degrees of nonclassicality and purities of the input states. The minimum and maximum amounts of attainable entanglement in the output state are found.     

Entanglement and disentanglement from cascade beam-splitter for squeezed vacuum state inputs

Properties of the entanglement at the outputs of a cascade beam-splitter are investigated for two single-mode squeezed vacuum state inputs. It is shown that the entanglement depends on the squeezing amplitudes of the input states and the reflection coefficients of the cascade beam-splitter, and the composite phase shift Δ between the cascade beam-splitter and the input fields has a great effect on the entanglement. In particular, the properties of the entanglement of a cascade beam-splitter differ from those of only one beam-splitter. A further method for manipulating entanglement by adjusting the parameters of the cascade beam-splitter and the input fields is proposed.     

Quantum teleportation of one－ and two－photon superposition states

Quantum teleportation of one- and two-photon superposition states based on EPR entanglement of continuous-wave two-mode squeezed state is discussed. The fidelities of teleportation axe deduced for two different input quantum states. The dependence of the fidelity on the parameters of EPR entanglement and the gain of the classical channels are shown numerically. Comparing with the teleportation of Fock state and coherent state, it is pointed out that for given EPR entanglement and classical gain, the higher the nonclassicality of the input state, the lower the accessible fidelity of teleportation.     

Entanglement properties in a system of a pairwise entangled state

Based on the quantum information theory, this paper has investigated the entanglement properties of a system which is composed of the two entangled two-level atoms interacting with the two-mode entangled coherent fields. The influences of the strength of light field and the two parameters of entanglement between the two-mode fields on the field entropy and on the negative eigenvalues of partial transposition of density matrix are discussed by using numerical calculations. The result shows that the entanglement properties in a system of a pairwise entangled states can be controlled by appropriately choosing the two parameters of entanglement between the two-mode entangled coherent fields and the strength of two light fields respectively.     

Maximal entanglement from photon-added nonlinear coherent states via unitary beam splitters

In this paper, we construct photon-added f-deformed coherent states （PAf-DCSs） for nonlinear bosonic fields by discussing Klauder＇s minimal set of conditions required to obtain coherent states. Using this set of nonlinear states, we propose a very useful scheme for generating the maximal amount of entanglement via unitary beam splitters for different strength regimes of the input field α, deformation q and excitation number m. Therefore, the possibility to create highly entangled states and to control the entanglement is proposed. Moreover, the condition for a maximal and separable output beam state is obtained. Finally, we examine the statistical properties of the PAf-DCSs through the Mandel parameter and exploit a connection between this quantity and the behavior variation of the output state entanglement. Our result may open new perspectives in different tasks of quantum information processing.     

The decoherence of quantum entanglement and teleportation in Bell-diagonal states

We study the dynamics of entanglement and teleportation in Bell-diagonal states. Using the concepts of concurrence and fidelity, the analytical expressions of the entanglement, the output entanglement and the average fidelity with decoherence are obtained for this model. We discover a class of initial states in which the output entanglement and the average fidelity are destroyed by decoherence. The quality of teleportation depends on the system parameters and time.     

Entanglement properties between two atoms in the binomial optical field interacting with two entangled atoms

The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.     

Quantum entanglement and nonlocality properties of two-mode Gaussian squeezed states

Quantum entanglement and nonlocality properties of a family of two-mode Gaussian pure states have been investigated. The results show that the entanglement of these states is determined by both the two-mode squeezing parameter and the difference of the two single-mode squeezing parameters. For the same two-mode squeezing parameter, these states show larger entanglement than the usual two-mode squeezed vacuum state. The violation of Bell inequality depends strongly on all the squeezing parameters of these states and disappears completely in the limit of large squeezing. In particular, these states can exhibit much stronger violation of local realism than two-mode squeezed vacuum state in the range of experimentally available squeezing values.     

Symmetric Telecloning and Entanglement Distribution of Spin Quantum States

We propose a physical realization of symmetric telecloning machine for spin quantum states. The concept of area average fidelity is introduced to describe the telecloning quality. It is indicated that for certain input states this quantity may come to an enough high level to satisfy the need of quantum information processing. We also study the properties of entanglement distribution via the spin chain for arbitrary two-qubit entangled pure states as inputs and find that the decay ratio of entanglement for the output states is only determined by the parameters of spin chain and waiting time, independent of the initial input states.     

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.     

Entanglement Properties of Output Field from Beam Splitter with the Generalized Two-Mode Squeezed Vacuum State Inputs

Entangling properties of output field from beam splitter are investigated with the generalized two-mode squeezed vacuum state inputs. It is found that the entanglement are not only strongly dependent on the squeezing parameters of the input state but also quite involved with the angular parameter of the beam splitter. By appropriately choosing the parameters of both input field and the beam splitter, the best entanglement can be obtained.     

纠缠压缩真空态的纠缠转移

通过分析光学分束器对压缩真空态光场的作用,发现如果分束器的输入光是两束具有同样振幅和相位的单模压缩真空态光场,则输出光为双模压缩真空态光场;若分束器的输入光是两束具有同样振幅但有π相位差的单模压缩真空态光场,则输出光仍为两束单模压缩真空态光场.对于双模压缩真空态光场,每个模中容纳的光子数可以是基数或偶数.而对于单模压缩真空态光场,每个模中只能包含偶数个光子.根据这些结果,提出了一个纠缠转移的方案.在这个方案中,两个纠缠压缩真空态光场被用作量子信道,通过利用光学分束器作用和光子数探测的方法,并在经典通讯的帮助下,实现了三个通讯伙伴之间的纠缠转移.     

利用分束器通过条件测量制备非经典光场态和量子纠缠态

把相干态和单粒子数态作为分束器的输入态，通过条件测量可以剪去输入相干态中的任意粒子数态，并研究了这些被剪切了的光场态的性质。结果显示剪去真空态和单粒子数态的输出态具有较强的压缩和亚泊松分布等非经典效应。把剪切了的输出态和真空态输入分束器，得到的输出态具有量子纠缠性质，从而制备出量子纠缠态，同时也验证了被剪切的输出态的非经典性。     

Engineering Two-Mode Non-Gaussian States with Vortex Structures Using a Beam Splitter

Vortex structure and entanglement properties of output field from a beam splitter are investigated. With a n-photon Fock state and a coherent state as the inputs, it is found that the output state before a beam splitter bears a vortex structure in quadrature space and is always entangled and non-classical based on the linear entropy criterion and the P-function analysis in phase space.     

Entangled phase states via quantum beam splitter

We study the entanglement effect of beam splitter on the temporally stable phase states. Specifically, we consider the eigenstates (phase states) of a unitary phase operator resulting from the polar decomposition of ladder operators of generalized Weyl-Heisenberg algebras possessing finite dimensional representation space. The linear entropy that measures the degree of entanglement at the output of the beam splitter is analytically obtained. We find that the entanglement is not only strongly dependent on the Hilbert space dimension but also quite related to strength the parameter ensuring the temporal stability of the phase states. Finally, we discuss the evolution of the entangled phase states.     

Quantum interference between a single-photon Fock state and a coherent state

We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for all passive and lossless optical four port devices. We show further how the results can be adapted to the case of the Mach-Zehnder interferometer. In addition we consider the case for which the single-photon Fock state is replaced with a general input state: a coherent input state displaces each general quantum state at the output port of a beam splitter with the displacement parameter being the amplitude of the coherent state.     

Quantum state engineering using conditional measurement on a beam splitter

State preparation via conditional output measurement on a beam splitter is studied, assuming the signal mode is mixed with a mode prepared in a Fock state and photon numbers are measured in one of the output channels. It is shown that the mode in the other output channel is prepared in either a photon-subtracted or a photon-added Jacobi polynomial state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output Fock state onto which it is projected. The properties of the conditional output states are studied for coherent and squeezed input states, and the probabilities of generating the states are calculated. Relations to other states, such as near-photon-number states and squeezed-state-excitations, are given and proposals are made for generating them by combining the scheme with others. Finally, effects of realistic photocounting and Fock-state preparation are discussed. Received: 17 March 1998 / Revised and Accepted: 8 May 1998