Complex Wavelet Transform of the Two-mode Quantum States

By employing the bipartite entangled state representation and the technique of integration within an ordered product of operators, the classical complex wavelet transform of a complex signal function can be recast to a matrix element of the squeezing-displacing operator U ₂(μ, σ) between the mother wavelet vector 〈ψ| and the two-mode quantum state vector |f〉 to be transformed. 〈ψ|U ₂(μ, σ)|f〉 can be considered as the spectrum for analyzing the two-mode quantum state |f〉. In this way, for some typical two-mode quantum states, such as two-mode coherent state and two-mode Fock state, we derive the complex wavelet transform spectrum and carry out the numerical calculation. This kind of wavelet-transform spectrum can be used to recognize quantum states.     

Pairwise Quantum Discord for a Symmetric Multi-Qubit System in Different Types of Noisy Channels

We study the pairwise quantum discord (QD) for a symmetric multi-qubit system in different types of noisy channels, such as phase-flip, amplitude damping, phase-damping, and depolarizing channels. Using the QD and geometric quantum discord (GMQD) to quantify quantum correlations, some analytical and numerical results are presented. The results show that, the QD dynamics is strongly related to the number of spin particles N as well as the initial parameter ?? of the one-axis twisting collective state. With the number of spin particles N increasing, the amount of the QD increases. However, when the amount of the QD arrives at a stable maximal value, the QD is independence of the number of spin particles N increasing. The behavior of the QD is symmetrical during a period 0 ≤ ?? ≤ 2π. Moreover, we compare the QD dynamics with the GMQD for a symmetric multi-qubit system in different types of noisy channels.     

Probabilistic Quantum Information Splitting Based on the Non-maximally Entangled Four-Qubit State

In this paper, we propose a scheme for quantum information splitting based on the non-maximally entangled four-qubit state in order to realize the splitting of the specific two-qubit state |ψ〉 _{A B} =x|00〉+y|11〉. The information splitter will safely share an state to the receiver with help of the controller. Through introducing an auxiliary system and applying several appropriate unitary transformations the information receiver can reconstruct the original state sent by the information splitter. Due to the non-maximally entangled four-qubit state, the total probability that the receiver obtains the original information is P. Furthermore, we discuss the relationship between the successful splitting probability and the concurrence of the entangled state and get a specific expression. In addition, the scheme is tested against external and internal attacks, and we define a function to characterise the security with the concurrence of the entanglement.     

Kraus Operator-Sum Solution to the Master Equation Describing the Single-Mode Cavity Driven by an Oscillating External Field in the Heat Reservoir

Exploiting the thermo entangled state approach, we successfully solve the master equation for describing the single-mode cavity driven by an oscillating external field in the heat reservoir and then get the analytical time-evolution rule for the density operator in the infinitive Kraus operator-sum representation. It is worth noting that the Kraus operator M _{l, m} is proved to be a trace-preserving quantum operation. As an application, the time-evolution for an initial coherent state ρ _|β〉 = |β〉〈β| in such an environment is investigated, which shows that the initial coherent state decays to a new mixed state as a result of thermal noise, however the coherence can still be reserved for amplitude damping.     

Teleportation of aTripartite Squeezed Entangled State Via EPR Entangled State with Continuous Variables

A scheme for teleporting an arbitrary tripartite entangled state is proposed when three bipartite entangled states (|η〉) with continuous variables are used as quantum channels. Quantum teleportation can be carried out successfully if the receiver adopts an appropriate unitary transformation. The calculation is greatly simplified by virtue of the Schmidt decompositions of both tripartite entangled state |p _t ,χ ₂,χ ₃〉 and |η〉. Any tripartite state which can be expanded in terms of |p _t ,χ ₂,χ ₃〉 may be teleported in this way due to the completeness of |p _t ,χ ₂,χ ₃〉.     

On the maximum admissible error and key compression degree in quantum cryptography on two nonorthogonal states

The extreme admissible error probability at the receiving end to which the secure key distribution is possible has been found. This result takes into account all possible attacks on the distributed key, including those that involve large quantum memory and the capability of an eavesdropper to perform collective measurements simultaneously over the entire transmitted sequence of quantum states. The critical error is independent of the parameters of a particular attack and is determined only in terms of the overlapping degree ε = |〈u₁|u₀〉¦ of information states and the fundamental functions of classical and quantum information theories. The latter functions are the capacity H(Q) of a classical binary communication channel and classical capacity \(\bar C(\varepsilon )\) of a binary quantum communication channel. The key compression degree after error correction is also expressed in terms of only the classical capacity \(\bar C(\varepsilon )\) of the quantum communication channel.     

Protecting Distribution Entanglement by Weak Measurement and Reversal under Various Decoherence Sources

Protection of entanglement from disturbance of the environment is an essential task marion processing. We examine the validity and limitation of the weak measurement and reversal in quantum infor- （WMR） operation in the protection of distributed entanglement from various decoherence sources. Since the entanglement variation can be investigated analytically for an arbitrarily entangled bipartite pure state under three kinds of typical noisy quantum channels, we show explicitly that the WMR operation indeed helps for protecting distributed entanglement from ampli- tude damping and phase damping, but not for depolarizing. Bxperimental feasibility for testing our results is discussed using current laboratory techniques.     

Population Dynamics of Excited Atoms in Dissipative Cavities

Population dynamics of excited atoms in dissipative cavities is investigated in this work. We present a method of controlling populations of excited atoms in dissipative cavities. For the initial state |ee〉_AB|00〉_ab, the repopulation of excited atoms can be obtained by using atom-cavity couplings and non-Markovian effects after the atomic excited energy decays to zero. For the initial state |gg〉_AB|11〉_ab, the two atoms can also be populated to the excited states from the initial ground states by using atom-cavity couplings and non-Markovian effects. And the stronger the atom-cavity coupling or the non-Markovian effect is, the larger the number of repopulation of excited atoms is. Particularly, when the atom-cavity coupling or the non-Markovian effect is very strong, the number of repopulation of excited atoms can be close to one in a short time and will tend to a steady value in a long time.     

Thermal Entanglement Between Atoms in the Four-Cavity Linear Chain Coupled by Single-Mode Fibers

Natural thermal entanglement between atoms of a linear arranged four coupled cavities system is studied. The results show that there is no thermal pairwise entanglement between atoms if atom-field interaction strength f or fiber-cavity coupling constant J equals to zero, both f and J can induce thermal pairwise entanglement in a certain range. Numerical simulations show that the nearest neighbor concurrence C_AB is always greater than alternate concurrence C_AC in the same condition. In addition, the effect of temperature T on the entanglement of alternate qubits is much stronger than the nearest neighbor qubits.     

Quantum Correlations of Two Relativistic Spin-12 Particles Under Noisy Channels

We study the quantum correlation dynamics of bipartite spin-\(\frac {1}{2}\) density matrices for two particles under Wigner rotations induced by Lorentz transformations which is transmitted through noisy channels. We compare quantum entanglement, geometric discord(GD), and quantum discord (QD) for bipartite relativistic spin-\(\frac {1}{2}\) states under noisy channels. We find out QD and GD tend to death asymptotically but a sudden change in the decay rate of the entanglement occurs under noisy channels. Also, bipartite relativistic spin density matrices are considered as a quantum channel for teleportation one-qubit state under the influence of depolarizing noise and compare fidelity for various velocities of observers.     

Laguerre-Polynomial-Weighted Two-Mode Squeezed State

We propose a new optical field named Laguerre-polynomial-weighted two-mode squeezed state. We find that such a state can be generated by passing the l-photon excited two-mode squeezed vacuum state C_la^?lS₂|00〉 through an single-mode amplitude damping channel. Physically, this paper actually is concerned what happens when both excitation and damping of photons co-exist for a two-mode squeezed state, e.g., dessipation of photon-added two-mode squeezed vacuum state. We employ the summation method within ordered product of operators and a new generating function formula about two-variable Hermite polynomials to proceed our discussion.     

Radiation of electromagnetic waves by a dipole in an external uniform electrostatic field

Exact solution for the electromagnetic field densities E and H of a dipole of uniformly accelerated point-charges with identical masses is discussed. It is shown that, for any fixed time t and a large distance R between the center of the dipole and the fieldpoint, |E| ~ R ^?4, |H| ~ R ^?5, while for large c|t| ~ R, |E| ~ |H| ~1/R as in spherical electromagnetic waves. Nevertheless, any irreversible radiation of electromagnetic waves is absent since the wave zone does not exist.     

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor ?? and relative coupling strength R=g₁/g₂ on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ_a),C(ρ_f),S(ρ_a)) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate ?? and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.     

Squeezing of Relative and Center-of-Orbit Coordinates of a Charged Particle by Step-Wise Variations of a Uniform Magnetic Field with an Arbitrary Linear Vector Potential

We consider a quantum charged particle moving in the xy plane under the action of a time-dependent magnetic field described by means of the linear vector potential A = H(t) [?y(1 + β), x(1 ? β)] /2 with a fixed parameter β. The systems with different values of β are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are ellipses for |β| < 1 and hyperbolas for |β| > 1. Using the approximation of the stepwise variation of the magnetic field H(t), we obtain explicit formulas describing the evolution of the principal squeezing in two pairs of noncommuting observables: the coordinates of the center of orbit and relative coordinates with respect to this center. Analysis of these formulas shows that no squeezing can arise for the circular gauge (β = 0). On the other hand, for any nonzero value of β, one can find the regimes of excitations resulting in some degree of squeezing in the both pairs. The maximum degree of squeezing can be obtained for the Landau gauge (|β| = 1) if the magnetic field is switched off and returns to the initial value after some time T, in the limit T → ∞.     

Quantification of Quantum Entanglement in a Multiparticle System of Two-Level Atoms Interacting with a Squeezed Vacuum State of the Radiation Field

We quantify multiparticle quantum entanglement in a system of N two-level atoms interacting with a squeezed vacuum state of the electromagnetic field. We calculate the amount of quantum entanglement present among one hundred such two-level atoms and also show the variation of that entanglement with the radiation field parameter. We show the continuous variation of the amount of quantum entanglement as we continuously increase the number of atoms from N = 2 to N = 100. We also discuss that the multiparticle correlations among the N two-level atoms are made up of all possible bipartite correlations among the N atoms.     

Persistence of quantum correlations in a XY spin-chain environment

Quantum correlations in a physical system are usually degraded whenever there is aninteraction with the environment. Here we consider the action of a XY spin-chain interactingwith a system of two qubits. Results are surprising for particular families of statessince their evolution does not destroy the presence of either entanglement or nonlocality,that is, those correlations persist for any possible configuration of theenvironment. In addition, we unveil the form of those states which, although being mixed,their entanglement implies nonlocality and vice versa. This finding constitutes anextension of the well-known Gisin Theorem for pure states of two qubits.The ensuing form will enable us to find the evolved entanglement and nonlocality in ananalytical fashion.     

Solar system constraints on asymptotically flat IR modified Hořava gravity through light deflection

In this paper, we study the motion of photons around a Kehagias–Sfetsos (KS) black hole and obtain constraints on IR modified Ho?ava gravity without cosmological constant (~Λ _W ). An analytic formula for the light deflection angle is obtained. For a propagating photon, the deflection angle δφ increases with large values of the Ho?ava gravity parameter ω. Under the UV limit \({\omega \longrightarrow \infty}\), deflection angle reduces to the result of usual Schwarzschild case, 4GM/R. It is also found that with increasing scale of astronomical observation system the Ho?ava–Lifshitz gravity should satisfy |ω M ²| > 1.1725 × 10^?16 with 12% precision for Earth system, |ω M ²| > 8.27649 × 10^?17 with 17% precision for Jupiter system and |ω M ²| > 8.27650 × 10^?15 with 0.17% precision for solar system.     

Quantum Cryptography,Quantum Communication,and Quantum Computer in a Noisy Environment

First, we study several information theories based on quantum computing in a desirable noiseless situation. (1) We present quantum key distribution based on Deutsch’s algorithm using an entangled state. (2) We discuss the fact that the Bernstein-Vazirani algorithm can be used for quantum communication including an error correction. Finally, we discuss the main result. We study the Bernstein-Vazirani algorithm in a noisy environment. The original algorithm determines a noiseless function. Here we consider the case that the function has an environmental noise. We introduce a noise term into the function f(x). So we have another noisy function g(x). The relation between them is g(x) = f(x) ± O(??). Here O(??) ? 1 is the noise term. The goal is to determine the noisy function g(x) with a success probability. The algorithm overcomes classical counterpart by a factor of N in a noisy environment.     

Global geometric entanglement and quantum phase transition in three-leg spin-3/2 Heisenberg tubes

Based on the tensor network representations, we have developed an efficient scheme to calculate the global geometric entanglement as a multipartite entanglement measure for the three-leg spin tubes. From the geometric entanglement, the phase diagram of a spin-3 / 2 isosceles triangle spin tube has been investigated varying the base interaction α. Two Berezinsky-Kosterlitz-Thouless phase transitions are estimated to be α_c1 ? 0.68 and α_c2 ? 3.85, respectively. Then, even though the spin tube is in gapless spin liquid phases for α<α_c1 and α >α_c2, the geometrical structure difference between the groundstate wavefunctions for the two regions is found to reflect the global geometric entanglement that contains bipartite and multipartite contributions. Further, the phase transition points from the von Neumann entropies and fidelity are consistent with that from the geometric entanglement. As a result, the global geometric entanglement can be used to explore a geometrical nature of quantum phases as well as an indicator for quantum phase transitions in many-body lattice systems.     

The Dynamics of Quantum Entanglement and General Quantum Correlations in the Double Tavis-Cumming Model

We study the dynamics of quantum correlations involving entanglement and discord of two pairs of two-level atoms in cavity QED. In the model, two atoms A and C are coupled with a single-mode cavity field via Tavis-Cumming interaction at one location, and the same for B and D at another location. The two locations are connected by the entanglement of the atoms AB and CD while there are no any direct interactions between them. Through comparing the robustness of entanglement and discord of the atoms in various initial conditions of cavities, it is shown the discord is more robust than the entanglement and would be useful in quantum information technology.