Influence of dephasing on the entanglement teleportation via a two-qubit Heisenberg XYZ system

We study the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence. The usefulness of such a system for performance of the quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation protocol T₁\mathcal{T}_1 is also investigated. The results depend on the initial conditions and the parameters of the system. The roles of system parameters such as the inhomogeneity of the magnetic field b and the spin-orbit interaction parameter D, in entanglement dynamics and fidelity of teleportation, are studied for both product and maximally entangled initial states of the resource. We show that for the product and maximally entangled initial states, increasing D amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of the teleportation. For a product initial state and specific interval of the magnetic field B, the asymptotic entanglement and hence the fidelity of teleportation can be improved by increasing B. The XY and XYZ Heisenberg systems provide a minimal resource entanglement, required for realizing efficient teleportation. Also, in the absence of the magnetic field, the degree of entanglement is preserved for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {00} \right\rangle \pm } \right|\left. {11} \right\rangle } \right)} \right.. The same is true for the maximally entangled initial states $\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right.$\left| {\psi \left. {\left( 0 \right)} \right\rangle = \frac{1} {{\sqrt 2 }}\left( {\left| {\left. {01} \right\rangle \pm } \right|\left. {10} \right\rangle } \right)} \right., in the absence of spin-orbit interaction D and the inhomogeneity parameter b. Therefore, it is possible to perform quantum teleportation protocol T₀\mathcal{T}_0 and entanglement teleportation T₁\mathcal{T}_1, with perfect quality, by choosing a proper set of parameters and employing one of these maximally entangled robust states as the initial state of the resource.     

Controlling on Entangled Decoherence by the Interaction Model Between Qubit and Environment

The entangling evolution of the coupled qubits interacting with non-Markov environment is investigated in terms of concurrence. The results show that the entanglement of quantum systems depends on not only the initial state of system but also the coupling ways between qubit and environment. It shows that: (1) when the system is initially in ( | 00 ?±| 11 ?)/?2( | 00 \rangle\pm| 11 \rangle)/\sqrt{2} state or in the mixed state which is produced by the state, if we can control the coupling between the qubits and the environment in a asymmetrical state, we can make the quantum system always in the entangled state. (2) For an initial state ( | 01 ?±| 10 ?)/?2( | 01 \rangle\pm| 10 \rangle)/\sqrt{2} or in its mixed state, in contrast, there will not be entangled death under the symmetric coupling. We also find that, in ( | 01 ?±| 10?)/?2( | 01 \rangle\pm| 10\rangle)/\sqrt{2} or in its mixed state, the stronger the interaction between qubits is, the better to struggle against entanglement sudden death is.     

Multipartite quantum correlations among atoms in QED cavities

We study the nonlocality dynamics for two models of atoms in cavity quantum electrodynamics (QED); the first model contains atoms in a single cavity undergoing nearest-neighbor interactions with no initial correlation, and the second contains atoms confined in n different and noninteracting cavities, all of which were initially prepared in a maximally correlated state of n qubits corresponding to the atomic degrees of freedom. The nonlocality evolution of the states in the second model shows that the corresponding maximal violation of a multipartite Bell inequality exhibits revivals at precise times, defining, nonlocality sudden deaths and nonlocality sudden rebirths, in analogy with entanglement. These quantum correlations are provided analytically for the second model to make the study more thorough. Differences in the first model regarding whether the array of atoms inside the cavity is arranged in a periodic or open fashion are crucial to the generation or redistribution of quantum correlations. This contribution paves the way to using the nonlocality multipartite correlation measure for describing the collective complex behavior displayed by slightly interacting cavity QED arrays.     

三比特类GHZ态的Bell型不等式和非定域性

研究了一般形式类GHZ(Greenberger-Horne-Zeilinger)态的共生纠缠度及非定域性, 给出了类GHZ纠缠态的共生纠缠、Mermin不等式和Svetlichny不等式的解析表达式, 并通过数值计算讨论纠缠与非定域性之间的关系. 结果表明, 类GHZ纠缠态的共生纠缠和两个Bell型不等式描述的非定域性是一致的, Bell算符及其参量, 能够明显展示量子态的非定域特性. 关键词： 量子信息 类GHZ态 共生纠缠 Bell型不等式     

Creating large NOON states with imperfect phase control

Optical NOON states ${{\left( {\left| {\left. {N,0} \right\rangle + } \right|\left. {0,N} \right\rangle } \right)} \mathord{\left/ {\vphantom {{\left( {\left| {\left. {N,0} \right\rangle + } \right|\left. {0,N} \right\rangle } \right)} {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }}${{\left( {\left| {\left. {N,0} \right\rangle + } \right|\left. {0,N} \right\rangle } \right)} \mathord{\left/ {\vphantom {{\left( {\left| {\left. {N,0} \right\rangle + } \right|\left. {0,N} \right\rangle } \right)} {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }} are an important resource for Heisenberg-limited metrology and quantum lithography. The only known methods for creating NOON states with arbitrary N via linear optics and projective measurements seem to have a limited range of application due to imperfect phase control. Here, we show that bootstrapping techniques can be used to create high-fidelity NOON states of arbitrary size.     

Polarization correlation in the two-photon decay of atomic hydrogen: nonlocality versus entanglement

From the work by Perrie et al. [Phys. Rev. Lett. 54, 1790 (1985)], photon pairs from the 2s _1/2 → 1s _1/2 (two-photon) decay of atomic hydrogen are known to be quantum mechanically correlated. In these experiments, the polarization states of the photons emitted in back-to-back geometry were shown to violate the Bell inequality as a qualitative sign of nonlocality and entanglement. In the present contribution, we analyze how these nonlocal quantum correlations, as given by the violation of the Bell inequality, differ from the concurrence as a true entanglement measure. Results are shown for both quantifiers in dependence of the decay geometry and the initial polarization of the atoms for the 2s _1/2 → 1s _1/2 and 3d _5/2 → 1s _1/2 two-photon decay of atomic hydrogen. These results display the difference between nonlocality and entanglement and, hence, may stimulate further experiments on nonlocal quantum correlations in atomic systems.     

Einstein-Podolsky-Rosen Steering for Mixed Entangled Coherent States

By using the Born Markovian master equation, we study the relationship among the Einstein–Podolsky–Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.     

Amplitude-squared squeezing in superposed coherent states

We study amplitude-squared squeezing of the Hermitian operator Z_θ=Z₁ cosθ+Z₂ sin θ, in the most general superposition state , of two coherent states and . Here operators Z_1,2 are defined by , a is annihilation operator, θ is angle, and complex numbers C_1,2 , α, β are arbitrary and only restriction on these is the normalization condition of the state . We define the condition for a state to be amplitude-squared squeezed for the operator Z_θ if squeezing parameter , where N=a⁺a and . We find maximum amplitude-squared squeezing of Z_θ in the superposed coherent state with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp [±i(π/4) + iθ/2], and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.     

Enhancing non-local correlations in the bipartite partitions of two qubit-system with non-mutual interaction

Several quantum-mechanical correlations, notably, quantum entanglement, measurement-induced nonlocality and Bell nonlocality are studied for a two qubit-system having no mutual interaction. Analytical expressions for the measures of these quantum-mechanical correlations of different bipartite partitions of the system are obtained, for initially two entangled qubits and the two photons are in their vacuum states. It is found that the qubits-fields interaction leads to the loss and gain of the initial quantum correlations. The lost initial quantum correlations transfer from the qubits to the cavity fields. It is found that the maximal violation of Bell’s inequality is occurring when the quantum correlations of both the logarithmic negativity and measurement-induced nonlocality reach particular values. The maximal violation of Bell’s inequality occurs only for certain bipartite partitions of the system. The frequency detuning leads to quick oscillations of the quantum correlations and inhibits their transfer from the qubits to the cavity modes. It is also found that the dynamical behavior of the quantum correlation clearly depends on the qubit distribution angle.     

通过设计量子库来调控量子比特间的Bell非定域性研究

量子系统间的Bell非定域性是一种比量子纠缠更为严格的量子关联,它在刻画多体量子关联有着不可或缺的作用.类似于量子纠缠,在开放两量子比特和三量子比特系统中的Bell非定域性可能会出现猝死现象.本文建议了一个可供选择的方案即在热库环境中通过增加辅助粒子来调控两量子比特和三量子比特间的Bell非定域性动力学.研究发现：通过调节辅助粒子数目,不仅两量子比特和三量子比特系统的Bell非定域性可以避免猝死现象的发生,而且在长时间极限下它能维持在一个较高水平.论文得到的结果将对多体量子系统间量子关联的调控和避免猝死现象等相关研究有积极的指导意义.     

Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states. we find a link to some entanglement measures through some new parameters (amplitudes of coherent states). Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of
entanglement by applying the formalism of Horodecki et al.     

Randomness versus nonlocality and entanglement

The outcomes obtained in Bell tests involving two-outcome measurements on two subsystems can, in principle, generate up to 2?bits of randomness. However, the maximal violation of the Clauser-Horne-Shimony-Holt inequality guarantees the generation of only 1.23?bits of randomness. We prove here that quantum correlations with arbitrarily little nonlocality and states with arbitrarily little entanglement can be used to certify that close to the maximum of 2?bits of randomness are produced. Our results show that nonlocality, entanglement, and randomness are inequivalent quantities. They also imply that device-independent quantum key distribution with an optimal key generation rate is possible by using almost-local correlations and that device-independent randomness generation with an optimal rate is possible with almost-local correlations and with almost-unentangled states.     

Fluctuations and a rigorous uncertainty relation of trigonometric operators of the phase and the number of photons of an electromagnetic field for general quantum superpositions of coherent states

The quantum-statistical properties of states of an electromagnetic field of general superpositions of coherent states of the form of N _α,β(α?+e ^iξ β? are investigated. Formulas for the fluctuations (variances) of Hermitian trigonometric phase field operators ? ≡ côs φ, ? ≡ sîn φ (the so-called “Susskind–Glogower operators”) are found. Expressions for the rigorous uncertainty relations (Cauchy inequalities) for operators of the number of photons and trigonometric phase operators, as well as for operators ? and ?, are found and analyzed. The states of amplitude \({N_{\alpha ,\beta }}\left( {\left| {{{\sqrt {ne} }^{i\varphi }}\rangle + {e^{i\xi }}\left| {{{\sqrt {{n_\beta }e} }^{i\varphi }}\rangle } \right.} \right.} \right)\), φ = φ_α = φ_β, and phase \({N_{\alpha ,\beta }}\left( {\left| {{{\sqrt {ne} }^{i{\varphi _\alpha }}}\rangle + {e^{i\xi }}\left| {{{\sqrt {ne} }^{i{\varphi _\beta }}}\rangle } \right.} \right.} \right)\), n = n _α = n _β, superpositions of coherent states are considered separately. The types of quantum superpositions of meso- and macroscales (n _α, n _β » 1) are found for which the sines and/or cosines of the phase of the field can be measured accurately, since, under certain conditions, the quantum fluctuations of these quantities are close to zero. A simultaneous accurate measurement of cosφ and sinφ is possible for amplitude superpositions, while an accurate measurement of one of these trigonometric phase functions is possible in the case of certain phase superpositions. Amplitude superpositions of coherent states with a vacuum state are quantum states of the field with a “maximum” level of the quantum uncertainty both in the case of a mesoscopic scale and in the case of a macroscopic scale of the field with an average number of photons n _α/β ≈ 0, n _β/α » 1.     

Quantum Entanglement Under Lorentz Transformation

We study the properties of quantum entanglement in moving frames, with a non-maximally entangled bipartite state: $|\phi\rangle=\sqrt{1-\varepsilon}|{\uparrow\uparrow}\rangle +\sqrt{\varepsilon}|{\downarrow\downarrow}\rangle$ , (0<ε<1). We calculate the concurrence of this state under Lorentz transformation and show that if the momenta part of the spin-1/2 pair is appropriately correlated, the concurrence is invariant ( $\mathcal {C}(\rho)=2\sqrt{\varepsilon-\varepsilon^{2}}$ ); despite the entanglement of this state is not maximal, there is no transfer of entanglement between spin and momentum.     

A Note on Quantum Bell Nonlocality and Quantum Entanglement for High Dimensional Quantum Systems

We study the Bell nonlocality of high dimensional quantum systems based on quantum entanglement. A quantitative relationship between the maximal expectation value B of Bell operators and the quantum entanglement concurrence C is obtained for even dimension pure states, with the upper and lower bounds of B governed by C.

     

Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε ⁻²|log ε|⁻¹ where Ω is the rotational velocity and the coupling parameter is written as ε ⁻² with ε≪1. Three critical speeds can be identified. At \varOmega = \varOmega_c1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for |loge| << \varOmega < \varOmega_c2 ~ e^-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For \varOmega 3 \varOmega _c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε ⁻²|log ε|⁻¹ vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at \varOmega = \varOmega_c3 ~ e^-2|loge|^-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break rotational symmetry in the whole parameter range, including the giant vortex phase.     

内禀退相干下Tavis-Cummings模型中原子的纠缠演化与贝尔不等式破坏

通过求解系统的Milburn方程，研究了两个二能级原子和单模场相互作用系统中原子间纠缠和贝尔不等式破坏随时间的演化特性，讨论了偶极相互作用、场与原子的失谐量对纠缠度以及贝尔不等式破坏的影响.结果表明：原子间偶极-偶极相互作用对纠缠度和贝尔不等式破坏有显著影响，失谐量增大会使两原子的纠缠度和贝尔不等式破坏变大，并且两原子所能达到稳定的纠缠受偶极相互作用系数与失谐量两者之差的影响.同时还发现两原子的纠缠与贝尔不等式破坏并不是单调的函数关系，很小的纠缠也可以产生贝尔不等式破坏. 关键词： Milburn理论 偶极-偶极相互作用 失谐量 贝尔不等式破坏     

Inequality relations for the hierarchy of quantum correlations in two-qubit systems

Entanglement, quantum steering and Bell nonlocality can be used to describe the distinct quantum correlations of quantum systems. Because of their different characteristics and application fields, how to divide them quantitatively and accurately becomes particularly important. Based on the sufficient and necessary criterion for quantum steering of an arbitrary two-qubit T-state, we derive the inequality relations between quantum steering and entanglement as well as between quantum steering and Bell nonlocality for the T-state. Additionally, we have verified those relations experimentally.