Quantum entanglement in the mode-mode competition system

Considering a two-level atom interacting with the competing two-mode field, this paper investigates the entanglement between the two-level atom and the two-mode field by using the quantum reduced entropy, and that between the two-mode field by using the quantum relative entropy of entanglement. It shows that the two kinds of entanglement are dependent on the relative coupling strength of atom-field and the atomic distribution, and exhibit the periodical evolution. The maximal atom-field entanglement state can be prepared via the appropriate selection of system parameters and interaction time.     

Analytic solutions for degenerate Raman-coupled model

The Raman-coupled interaction between an atom and a single mode of a cavity field is studied. For the cases in which a light field is initially in a coherent state and in a thermal state separately, we have derived the analytic expressions for the time evolutions of atomic population difference W, modulus B of the Bloch vector, and entropy E. We find that the time evolutions of these quantities are periodic with a period of π. The maxima of W and B appear at the scaled interaction time points τ- = kπ（k = 0, 1, 2,...）. At these time points, E = 0, which shows that the atom and the field are not entangled. Between these time points, E ≠ 0, which means that the atom and the field are entangled. When the field is initially in a coherent state, near the maxima, the envelope of W is a Gaussian function with a variance of 1/（4n^-）（n^- is the mean number of photons）. Under the envelope, W oscillates at a frequency of n^-/π. When the field is initially in a thermal state, near the maxima, W is a Lorentz function with a width of 1/n^-.     

Entanglement and quantum phase transition in alternating XY spin chain with next-nearest neighbouring interactions

By using the method of density-matrix renormalization-group to solve the different spin spin correlation functions, the nearest-neighbouring entanglement （NNE） and the next-nearest-neighbouring entanglement （NNNE） of one-dimensional alternating Heisenberg XY spin chain are investigated in the presence of alternating the-nearestneighbouring interaction of exchange couplings, external magnetic fields and the next-nearest neighbouring interaction. For a dimerised ferromagnetic spin chain, the NNNE appears only above a critical dimerized interaction, meanwhile, the dimerized interaction a effects a quantum phase transition point and improves the NNNE to a large extent. We also study the effect of ferromagnetic or antiferromagnetic next-nearest neighbouring （NNN） interaction on the dynamics of NNE and NNNE. The ferromagnetic NNN interaction increases and shrinks the NNE below and above a critical frustrated interaction respectively, while the antiferromagnetic NNN interaction always reduces the NNE. The antiferromagnetic NNN interaction results in a large value of NNNE compared with the case where the NNN interaction is ferromagnetic.     

Quantum phase transition and entanglement in Li atom system

By use of the exact diagonalization method, the quantum phase transition and entanglement in a 6-Li atom system are studied. It is found that entanglement appears before the quantum phase transition and disappears after it in this exactly solvable quantum system. The present results show that the von Neumann entropy, as a measure of entanglement, may reveal the quantum phase transition in this model.     

Entanglement of Resonantly Coupled Field Modes in Cavities with Vibrating Boundaries

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropy coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered — a three-dimensional cavity possessing eigenfrequencies ₃ = 3₁, whose wall oscillates at the frequency _w = 2₁, and a one-dimensional (Fabry–Perot) cavity with an equidistant spectrum _n = n₁ where the distance between perfect mirrors oscillates at the frequencies ₁ and 2₁. The behavior of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except some specific situations where the covariance entanglement coefficient based on traces of covariance submatrices seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field, namely, vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states, are considered.     

Entanglement reciprocation between two charge qubits and two-cavity field

We propose a simple scheme to generate two-mode entangled coherent state in two separated cavities and realize the entanglement reciprocation between the superconducting charge qubits and continuous-variable system. By measuring the state of charge qubits, we find that the entanglement of two charge qubits, which are initially prepared in the maximally entangled state, can be transferred to the two-cavity field, and at this time the two-cavity field is in the entangled coherent state. We also find that the entanglement can be retrieved back to the two charge qubits after measuring the state of the two-cavity field.      

A Scheme for Physical Implementation of a Ququadrit Quantum Computation with Cooled-Trapped Ions

The physics realization of a ququadrit quantum computation with cooled trapped ¹³⁸Ba⁺ ions in a Paul trap is investigated. The ground state level 6² S_1/2(m = −1/2) and three metastable levels: 5² D_3/2(m = −1/2), 5² D_5/2(m = −1/2), and 5² D_5/2(m = 1/2), of the fine-structure of the ¹³⁸Ba⁺ ion, are used to store the quantum information of ququadrits. The use of coherent manipulation of populations in single ququadrit, being a four-dimensional Hilbert space, produces a discrete Fourier transform and the manipulation of the first red band transitions with the introduction of an ancillary quantum channel between two ququadrits generates a conditional phase gate. The combination of the both above results in a universal two-ququadrit gate, called XOR⁽⁴⁾ gate corresponding to the controlled-NOT gate operation in qubit systems. The implementation of quantum Fourier transform for n ququadrits is performed by means of the conditional phase-shift gate. The feasibility of physical realization of ququadrit quantum computation with cooled-trapped ¹³⁸Ba⁺ ions is detailed analyzed and described, and the theoretical detection method of logical states is given. Higher entanglement between ququadrits than qutrits or qubits and more security of ququadrit quantum cryptography than qutrit's or qutrit's will lead to more extensive applications ququadrits in quantum information fields. In particular, it is pointed out that this scheme should be the highest dimensional quantum computation in cooled-trapped ions, the entanglement between ququadrits should be the highest dimensional entanglement in it, and the ququadrit quantum cryptography should be the most secure cryptography protocol in it.     

Information Theories with Adversaries,Intrinsic Information,and Entanglement

There are aspects of privacy theory that are analogous to quantum theory. In particular one can define distillable key and key cost in parallel to distillable entanglement and entanglement cost. We present here classical privacy theory as a particular case of information theory with adversaries, where similar general laws hold as in entanglement theory. We place the result of Renner and Wolf—that intrinsic information is lower bound for key cost—into this general formalism. Then we show that the question of whether intrinsic information is equal to key cost is equivalent to the question of whether Alice and Bob can create a distribution product with Eve using I_M bits of secret key. We also propose a natural analogue of relative entropy of entanglement in privacy theory and show that it is equal to the intrinsic information. We also provide a formula analogous to the entanglement of formation for classical distributions. It is our pleasure to dedicate this paper to Asher Peres on the occasion of his seventieth birthday.     

Quantum Mechanics is About Quantum Information

I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive---just as, following Einsteins special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical entity in its own right.     

What’s Wrong with Einstein’s 1927 Hidden-Variable Interpretation of Quantum Mechanics?

Einsteins unpublished 1927 deterministic trajectory interpretation of quantum mechanics is critically examined, in particular with regard to the reason given by Einstein for rejecting his theory. It is shown that the aspect Einstein found objectionable—the mutual dependence of the motions of particles when the (many-body) wavefunction factorises—is a generic attribute of his theory but that this feature may be removed by modifying Einsteins method in either of two ways: using a suggestion of Grommer or, in a physically important special case, using a simpler technique. It is emphasized though that the presence or absence of the interdependence property does not determine the acceptability of a trajectory theory. It is shown that there are other grounds for rejecting Einsteins theory (and the two modified theories), to do with its domain of applicability and compatibility with empirical predictions. That Einsteins reason for rejection is not a priori grounds for discarding a trajectory theory is demonstrated by reference to an alternative deterministic trajectory theory that displays similar particle interdependence yet is compatible with quantum predictions.PACS: 03.65.Bz.Essay written in memory of J.T. Cushing.