Spin geometry of entangled qubits under bilocal decoherence modes

The Lindblad generators of the master equation define which kind of decoherence happens in an open quantum system. We are working with a two qubit system and choose the generators to be projection operators on the eigenstates of the system and unitary bilocal rotations of them. The resulting decoherence modes are studied in detail. Besides the general solutions we investigate the special case of maximally entangled states—the Bell singlet states. The results are depicted in the so-called spin geometry picture which allows to illustrate the evolution of the (nonlocal) correlations stored in a certain state. The question for which conditions the path traced out in the geometric picture depends only on the relative angle between the bilocal rotations is addressed.     

New approach for solving the Wigner function from the Husimi function in the two-mode entangled state representation

We introduce a new method to calculate the Wigner function when its corresponding Husimi function is given. A new formula is derived for calculating conveniently the Wigner function in two-mode entangled state representation. As application, we derive Wigner functions of some quantum states, such as two-mode entangled state, the electron's two-mode squeezed canonical coherent state, and the electron's coordinate eigenstate.     

The effect and control on remaining the quantum correlation by the coupling symmetry between qubits and the bath

We study the dynamic evolution of quantum correlation of two interacting coupled qubits system in non-Markov environment, and quantify the quantum correlation using concurrence and quantum discord. We find that although both of them are physical quantities which measure the system characteristics of the quantum correlations, the quantum discord is more robust than concurrence, since it can keep a positive value even when the ESD happens. The quantum correlation of quantum system not only depends on the initial state but also strongly depends on the coupling ways between qubits and environment. For the given initial state, by keeping the coupling between qubits and environment in completely symmetric, we can completely avoid the effect the decoherence influenced on the quantum correlation and effectively prolong the survival time of quantum discord and concurrence. We also find that the stronger the interaction between qubits is, the more conducive the death of the quantum correlation is resisted.     

Newton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representations

Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac’s symbols (ket versus bra, e.g., |q〉〈q| of continuous parameter q) in quantum mechanics are usually not commutative. Therefore, integrations over the operators of type |〉〈| cannot be directly performed by Newton-Leibniz rule. We invented an innovative technique of integration within an ordered product (IWOP) of operators that made the integration of non-commutative operators possible. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac’s symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.     

Sudden death time of two-qubit entanglement in a noisy environment

We present a simple equation to predict the sudden death time of two-qubit entanglement in a noisy environment. This result is valid for all two-qubit systems, no matter what kind of noise is considered.     

GHZ argument for four-qubit entangled states in the presence of white and colored noise

Greenberger-Horn-Zeilinger (GHZ) argument of nonlocality without inequalities is extended to the case of four-qubit mixed states. Three different kinds of entangled states are analyzed in presence of white and colored noise. The nonlocality properties of these states will be weakened and destroyed by the noise. We found that all these states have the same ability to resist the influence of white noise, while the cluster state is the most robust against colored noise.     

Characteristic time and maximum mixedness: Single mode Gaussian states in dissipative channels

We derive an upper limit for the mixedness of single bosonic mode Gaussian states propagating in dissipative channels. It is a function of the initial squeezing and temperature of the channel only. Moreover the time at which von Neumann's entropy reaches its maximum value coincides with that of complete loss of coherence, thus defining a quantum-classical transition.     

Entanglements induced by cavity interacting with two-coupled atoms

We consider a quantum optics model where the cavity interacts with two-coupled atoms. The atom-atom entanglement, atoms-cavity entanglement and the mixture for the two atoms are investigated, and discuss the effects of the initial conditions, atom-atom coupling and the mean number of photons on the entanglements and mixture. We find that atom-atom coupling plays an important role in the entanglement and mixture. Numerical results show that under some conditions the phenomena of “entanglement sudden death” and “entanglement collapse and revival” emerge.     

Sudden death and birth of entanglement beyond the Markovian approximation

We investigate the entanglement dynamics of two initially entangled qubits interacting independently with two uncorrelated reservoirs beyond the Markovian approximation. Quite different from the Markovian reservoirs [C.E. López, et al., Phys. Rev. Lett. 101 (2008) 080503], we find that entanglement sudden birth (ESB) of the two reservoirs occurs without certain symmetry with respect to the entanglement sudden death (ESD) of the two qubits. A phenomenological interpretation of entanglement revival is also given.     

Control of the entanglement of a two-level atom in a dissipative cavity via a classical field

We investigate the entanglement dynamics and purity of a two-level atom, which is additionally driven by a classical field, interacting with a coherent field in a dissipative environment. It is shown that the amount of entanglement and the purity of the system can be improved by controlling the classical field.     

All-versus-nothing inseparability for two pairs of entangled atoms

It is shown that Cabello’s nonlocality without inequalities for two pairs of singlet states [A. Callebo, Phys. Rev. Lett. 87, 010403 (2001)] can be realized in two pairs of trapped atoms based on Innsbruck ion group. The reasoning mainly lies in that controlled NOT (CNOT) gate can be realized between two atoms in ion trap.     

An analytical description of the atomic information entropy in a multi-level system

We construct a complete representation of the atomic information entropy of an arbitrary multi-level system. Our approach is applicable to all scenarios in which the quantum state shared by a single particle and fields is known. As illustrations we apply our findings to a single four-level atom strongly coupled to a cavity field and driven by a coherent laser field. In this framework, we discuss connections with entanglement frustration and entropic forms. We conclude by showing how the atomic information entropy can be extended to examine entanglement in multi-level atomic systems.     

Measurement-induced nonlocality and geometric quantum discord in two SC-charge qubits

By using geometric quantum discord and measurement-induced nonlocality, quantum correlations are investigated for two superconducting (SC) charge qubits that share a large Josephson junction where the field is assumed to be prepared initially in a coherent state. It is found that the difference between measure measurement-induced nonlocality and geometric quantum discord, of the final state of the two SC-charge qubits system which is especial case of X-states, is equal to a constant value. It is found that the quantum correlations and entanglement of the qubits are very sensitive to the mean number of the coherent photons. The entanglement exists in small intervals of death quantum discord and measurement-induced nonlocality. This is further evidence in support of the fact that quantum correlation and entanglement are not synonymous.     

Qubit disentanglement in local squeezed reservoirs

We consider the influence of the local squeezed vacuum fields on two initially entangled two-qubit system. By considering the upper bound of entanglement under time evolution, we find that the decay of the quantum entanglement shows different behavior for different time scales (t?max{(2βA)⁻¹,(2βB)⁻¹}$t?\max \{{(2{\beta }_A)}^{\mathrm{-1}},{(2{\beta }_B)}^{\mathrm{-1}}\}$ and t?min{(2βA)⁻¹,(2βB)⁻¹}$t?\min \{{(2{\beta }_A)}^{\mathrm{-1}},{(2{\beta }_B)}^{\mathrm{-1}}\}$). The relative phase of the squeezing environment can also affect the entanglement dynamics profoundly.     

A revised controlled deterministic secure quantum communication with five-photon entangled state

A revised controlled deterministic secure quantum communication protocol using five-photon entangled state is proposed. It amends the security loopholes pointed by Qin et al. in [S.J. Qin, Q.Y. Wen, L.M. Meng, F.C. Zhu, Opt. Commun. 282 (2009) 2656] in the original protocol proposed by Xiu et al. in [X.M. Xiu, L. Dong, Y.J. Gao, F. Chi, Opt. Commun. 282 (2009) 333]. The security loopholes are solved by using order rearrangement of transmission photons and two-step security test.     

Local transformations of superpositions of entangled states

Suppose that we have two entangled states |?₁〉, |ψ₁〉 that cannot be converted to any of other two states |?₂〉, |ψ₂〉 by local operations and classical communication. We analyze the possibility of locally transforming a superposition of |?₁〉 and |ψ₁〉 into a superposition of |?₂〉 and |ψ₂〉. By using the Nielsen's theorem we find the necessary and sufficient conditions for this conversion to be performed.     

Deterministic secure quantum communication using four-particle genuine entangled state and entanglement swapping

A deterministic secure quantum communication scheme using entanglement swapping is proposed. The sender prepares four-particle genuine entangled states and sends two particles in each state to the receiver and remains the rest particles. If the quantum channel is secure, they begin to communicate. After their four-particle projective measurements, the receiver can obtain the secret information according to his measurement outcomes and classical information from the sender. Using entanglement swapping, there are no particles carrying secret information to be transmitted.     

A linear optical protocol of random quantum key distribution by using polarization entangled photons

Utilized polarization entangled photons, a linear optical protocol for generating random quantum key distribution (QKD) is proposed, which is made up of EPR-source, linear optical elements, and conventional photon detectors. It is shown that total efficiency of QKD η=100% in theory.     

On Wigner functions and a damped star product in dissipative phase-space quantum mechanics

Dito and Turrubiates recently introduced an interesting model of the dissipative quantum mechanics of a damped harmonic oscillator in phase space. Its key ingredient is a non-Hermitian deformation of the Moyal star product with the damping constant as deformation parameter. We compare the Dito-Turrubiates scheme with phase-space quantum mechanics (or deformation quantization) based on other star products, and extend it to incorporate Wigner functions. The deformed (or damped) star product is related to a complex Hamiltonian, and so necessitates a modified equation of motion involving complex conjugation. We find that with this change the Wigner function satisfies the classical equation of motion. This seems appropriate since non-dissipative systems with quadratic Hamiltonians share this property.     

Entanglement and sudden death of two two-level atoms interacting with a cavity field in presence of degenerate parametric amplifier

In the presence of degenerate two-photon transitions the problem of the interaction between two two-level atoms and a single-mode is considered. Near resonance case, a closed form of the analytic solution for the wave function is obtained. The entanglement between an atom and field in the interacting system is studied by using the change in atomic and field entropies. The relationship between entropy changes and concurrence entanglement is discussed. Our results show that the behavior of the entropy change in agreement with the behavior of the concurrence to measure the entanglement between two subsystem structures.