Optimal Remote Preparation of a Four-Qubit Entangled Cluster-Type State Via Two Non-Maximally Entangled GHZ-Type States

We devise an highly efficient protocol for remotely preparing a four-qubit entangled cluster-type state. In this protocol, two non-maximally entangled GHZ-type states are employed to link the sender Alice and the receiver Bob, and the to-be-prepared state can be reconstructed successfully with the probability of (b₁b₂)² in general case. Then to achieve our concerns of constructing efficient remote preparation with higher success probability, some special ensembles of four-qubit states are minutely investigated. As a result, it is shown that the total probability of the RSP protocol, in these particular cases, can be improved to twice or even fourfold as that in general case.     

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〉.     

Protecting Distribution Entanglement for Two-Qubit State Using Weak Measurement and Reversal

Protection of entanglement from disturbance of the environment is an essential task in quantum information processing. We investigate the effect of the weak measurement and reversal (WMR) on the protection of the entanglement for an arbitrarily entangled two-qubit pure state from these three typical quantum noisy channels, i.e., amplitude damping channel, phase damping channel and depolarizing quantum channel. Given the parameters of the Bell-like initial qubits’ state |ψ〉 = a|00〉 + d|11〉, it is found that the WMR operation indeed helps for protecting distributed entanglement from the above three noisy quantum channels. But for the Bell-like initial qubits’ state |?〉 = b|01〉 + c|10〉, the WMR operation only protects entanglement in the amplitude damping channel, not for the phase damping and depolarizing quantum channels. In addition, we discuss how the concurrence and the success probability behave with adjusting the weak or the reversal weak measurement strength.     

The New Multipartite Squeezing Operator and Some of its Properties

In this paper, we introduce a pair of mutually conjugate multipartite entangled state representations for defining the squeezing operator of entangled multipartite S_n(λ) which involves an n-mode bosonic operator realization of the SU(1,1) Lie algebra. This operator squeezes the multipartite entangled state in a natural way. We discuss the transform properties of a_j and \(a_{j}^{\dagger }\) under the operation of S_n(λ) and derive the interaction Hamiltonian which can generate such an evolution. In addition, the corresponding multipartite squeezed vacuum state |λ〉 is obtained. Based on this, the variances of the n-mode quadratures in |λ〉 are evaluated and the violation of the Bell inequality for |λ〉 is examined by using the formalism of Wigner representation.     

Remote State Preparation of a Two-Atom Entangled State in Cavity QED

A physical scheme for remotely preparing a diatomic entangled state based on the cavity QED technique is presented in this paper. The quantum channel is composed of a two-atom entangled state and a three-atom entangled W state. The non-resonant interaction between two atoms and cavity is utilized at sender’s side to distribute the information among the quantum channel, and the original state can be transmitted to either one of the two receivers. It shows that an extra cavity and an atom are needed at the final receiver’s side as an auxiliary system if the non-maximally entangled states are worked as the quantum channel. The total success probabilities for the two receivers are not equal to each other except that the states of the quantum channel are maximally entangled.     

Deterministic Joint Remote Preparation of a Four-Qubit Cluster-Type State via GHZ States

A scheme for the deterministic joint remote preparation of a four-qubit cluster-type state using only two Greenberger-Horne-Zeilinger (GHZ) states as quantum channels is presented. In this scheme, the first sender performs a two-qubit projective measurement according to the real coefficient of the desired state. Then, the other sender utilizes the measurement result and the complex coefficient to perform another projective measurement. To obtain the desired state, the receiver applies appropriate unitary operations to his/her own two qubits and two CNOT operations to the two ancillary ones. Most interestingly, our scheme can achieve unit success probability, i.e., P _{s u c} =1. Furthermore, comparison reveals that the efficiency is higher than that of most other analogous schemes.     

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.     

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.     

A probabilistic quantum communication protocol using mixed entangled channel

Qubits are realized as polarization state of photons or as superpositions of the spin states of electrons. In this paper we propose a scheme to probabilistically teleport an unknown arbitrary two-qubit state using a non-maximally entangled GHZ-like state and a non-maximally Bell state simultaneously as quantum channels. We also discuss the success probability of our scheme. We perform POVM in the protocol which is operationally advantageous. In our scheme we show that the non-maximal quantum resources perform better than maximal resources.     

Two-way quantum communication: Generalization of secure quantum information exchange to quantum network

The idea of secure quantum information exchange (SQIE) [J. Phys. B: At. Mol. Opt. Phys.44, 115504 (2011)] is introduced for the secure exchange of single qubit information states between two legitimate users, Alice and Bob. In the present paper, we extend this original SQIE protocol by presenting a scheme, which enables the secure exchange of n-single qubit information states among the n nodes of a quantum network, with the aid of a special kind of 4n-qubit entangled state and the classical assistance of an extra participant Charlie. For experimental realization of our extended SQIE protocol, we suggest an efficient scheme for the generation of a special kind of 4n-qubit entangled state using the interaction between highly detuned Λ-type three-level atoms and optical coherent field. Further, by discussing the various experimental parameters, we show that the special kind 4n-qubit entangled state can be generated with the presently available technology.     

Tripartite Quantum Controlled Teleportation via Seven-Qubit Cluster State

In this paper, a theoretical scheme for tripartite quantum controlled teleportation is presented using the entanglement property of seven-qubit cluster state. This means that Alice wants to transmit a entangled state of particle a to Bob, Charlie wants to transmit a entangled state of particle b to David and Edison wants to transmit a entangled state of particle c to Ford via the control of the supervisor. In the end, we compared the aspects of quantum resource consumption, operation complexity, classical resource consumption, quantum information bits transmitted, success probability and efficiency with other schemes.     

Deterministic Remote Preparation of a Four-Qubit Cluster-Type Entangled State

We propose a scheme for remotely preparing a four-qubit cluster-type state with complex coefficients by using six EPR pairs as the quantum channel. To complete the remote state preparation scheme, a novel set of four-qubit mutually orthogonal basis vectors has been introduced. It is shown that, after the sender performs two different four-qubit projective measurements, the receiver can reconstruct the original state (to be prepared remotely) with unit successful probability. Moreover, the scheme is also generalized to the case that non-maximally two-qubit entangled states are taken as the quantum channel.     

Photon Excitations Excitated the Sqeezing Properties of the Excited Entangled Coherent States

In our previous paper, we have introduced a new kind of continuous-variable-type entangled states, called double-mode excited entangled coherent states. In this paper, we study sum squeezing properties of such excited entangled coherent states. We focus on discussing the influence of photon excitations on sum squeezing properties. It is found that the photon excitations seriously affected sqeezing properties of the excited entangled coherent states. With increasing the number of the photon excitations m, the higher-order terms move away from its initial state |ψ ₀〉 and the degrees of sum squeezing are increasing. In this sense, it implies that the photon excitations excitated the sum sqeezing properties of the double-mode excited entangled coherent states.     

Maximizing Complementary Quantities by Projective Measurements

In this work, we study the so-called quantitative complementarity quantities. We focus in the following physical situation: two qubits (q _A and q _B ) are initially in a maximally entangled state. One of them (q _B ) interacts with a N-qubit system (R). After the interaction, projective measurements are performed on each of the qubits of R, in a basis that is chosen after independent optimization procedures: maximization of the visibility, the concurrence, and the predictability. For a specific maximization procedure, we study in detail how each of the complementary quantities behave, conditioned on the intensity of the coupling between q _B and the N qubits. We show that, if the coupling is sufficiently “strong,” independent of the maximization procedure, the concurrence tends to decay quickly. Interestingly enough, the behavior of the concurrence in this model is similar to the entanglement dynamics of a two qubit system subjected to a thermal reservoir, despite that we consider finite N. However, the visibility shows a different behavior: its maximization is more efficient for stronger coupling constants. Moreover, we investigate how the distinguishability, or the information stored in different parts of the system, is distributed for different couplings.     

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.     

Analysis of Control Power in Controlled Remote State Preparation Schemes

We quantify and analyze the controller’s power in controlled remote state preparation schemes. Our analysis provides a lower bound on the control power required for controlled remote preparation of arbitrary D-dimensional states. We evaluate several existing controlled remote state preparation protocols and show that some proposed non-maximally entangled channels are not suitable for perfect controlled remote preparation of arbitrary quantum states from the controller’s point of view. We find that for remotely preparing D-dimensional states, the entropy of each controller should be no less than log2D bits. Our new criteria are not only useful for evaluating controlled remote state preparation schemes but can also be used for other controlled quantum communication schemes.     

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.     

Majorana neutrinos, <Emphasis Type="Italic">CP</Emphasis> violation,neutrinoless double beta and tritium beta decays

If the present or upcoming searches for neutrinoless double beta ((ββ)_0ν) decay give a positive result, the Majorana nature of massive neutrinos will be established. From the determination of the value of the (ββ)_0ν-decay effective Majorana mass parameter (|〈m〉|), it would be possible to obtain information on the type of neutrino mass spectrum. Assuming 3-ν mixing and massive Majorana neutrinos, we discuss the information that a measurement of, or an upper bound on, |〈m〉| can provide on the value of the lightest neutrino mass m₁. With additional data on the neutrino masses obtained in ³H β-decay experiments, it might be possible to establish whether the CP symmetry is violated in the lepton sector. This would require very high precision measurements. If CP invariance holds, the allowed patterns of the relative CP parities of the massive Majorana neutrinos would be determined.     

Teleportation of Three-Particle W State

We present two schemes for teleporting a three-particle W state by using four-particle state. We consider that the quantum channel is a maximally entangled state (four-particle cluster state) or a non-maximally entangled state. In our schemes, it is necessary to introduce additional particle and construct unitary transformation for realize perfect or probabilistic teleportation of the three-particle W state. In order to transmit target state successfully, Alice firstly performs two controlled-NOT on the initial state. The success probabilities of our two schemes are 1 and 4α ², respectively. Compared with other schemes proposed before, our scheme has higher efficiency.     

Nonlinear interference in a mean-field quantum model

Using similar nonlinear stationary mean-field models for both a 2D axisymmetricalBose-Einstein Condensate and an electron pair in a parabolic trap, we propose to describethe original many-particle ground state as a one-particle mixed state (in contrast to apure state), i.e. as a statistical ensemble of several one-particle quantum states. Thesequantum states are the eigenfunctions of the corresponding stationary nonlinearSchrödinger equation (hence called “nonlinear eigenstates”). Due to their nonlinearity,they are not orthogonal. Therefore, taking the simple example of a two-level system, weshow that each of these two nonlinear eigenstates |i? and|j? occurs with a probability (or statistical weight) that isdefined by their non-orthogonality ?i|j? 0. We givethe corresponding density matrix. We search for physical grounds in the interpretation ofour two main results, namely, a quantum-classical nonlinear transition and theinterference between two “nonlinear eigenstates”.