Azeddine Messikh

Entanglement and spin squeezing in the two-atom Dicke model

We analyse the relation between the entanglement and the spin-squeezing parameter in the two-atom Dicke model and identify the source of the discrepancy recently reported by Banerjee (2001 Preprint quant-ph/0110032) and Zhou et al (2002 J. Opt. B. Quantum Semiclass. Opt. 4 425), namely that one can observe entanglement without spin squeezing. Our calculations demonstrate that there are two criteria for entanglement, one associated with the two-photon coherences that create two-photon entangled states, and the other associated with populations of the collective states. We find that the spin-squeezing parameter correctly predicts entanglement in the two-atom Dicke system only if it is associated with two-photon entangled states, but fails to predict entanglement when it is associated with the entangled symmetric state. This explicitly identifies the source of the discrepancy and explains why the system can be entangled without spin squeezing. We illustrate these findings with three examples of the interaction of the system with thermal, classical squeezed vacuum, and quantum squeezed vacuum fields.

Effect of dephasing on single-qubit rotation gates

In this paper we investigate the effect of dephasing on the performance of the quantum rotation gate implemented by adiabatic passage and static laser pulses proposed in Lacour et al (2006 Opt. Commun. 264 362). We show that in an open system, where the three-level lambda system is subjected to dephasing of its ground states, the dephasing will introduce additional dynamic phases which cannot be recompensated as in the closed system. We analyse the evolution of the population by using the quantum jump approach. The results are obtained assuming realistic dephasing rates ?0 1.

Generative Power and Closure Properties of Watson-Crick Grammars

We define WK linear grammars, as an extension of WK regular grammars with linear grammar rules, and WK context-free grammars, thus investigating their computational power and closure properties. We show that WK linear grammars can generate some context-sensitive languages. Moreover, we demonstrate that the family of WK regular languages is the proper subset of the family of WK linear languages, but it is not comparable with the family of linear languages. We also establish that the Watson-Crick regular grammars are closed under almost all of the main closure operations.

Dynamic batch rekeying scheme using Multiple Logical key trees for secure multicast communication

A group key management has an important role in multicast security in order to achieve data integrity and confidentiality. The session key is a common secret key for a group of users in key trees that is shared securely and efficiently among them. It is used to encrypt other session keys and transmitted data in order to protect group communication. This paper proposed a new key management protocol using Multiple Logical key trees for dynamic groups. To minimize the communication overhead of rekeying process, a one-way key derivation are integrated with multiple logical key trees. New keys created by the server of the key tree are not sent to the members who are able to derive their own keys. As a result each rekeying process requires less number of encrypted keys sent within the group tree. The performance analysis of the proposed scheme shows that it has less communication cost than the other compared protocols.

Quantum properties of the three-mode squeezed operator: Triply concurrent parametric amplifiers

Abstract In this paper, we study the quantum properties of the three-mode squeezed operator. This operator is constructed from the optical parametric oscillator based on the three concurrent χ (2) nonlinearities. We give a complete treatment for this operator including the symmetric and asymmetric nonlinearity cases. The action of the operator on the number and coherent states is studied in the framework of squeezing, second-order correlation function, Cauchy–Schwartz inequality and single-mode quasiprobability function. The nonclassical effects are remarkable in all these quantities. We show that the nonclassical effects generated by the asymmetric case–for certain values of the system parameters–are greater than those of the symmetric one. This reflects the important role for the asymmetry in the system. Moreover, the system can generate particular types of the superposition states.

Watson–Crick Context-Free Grammars: Grammar Simplifications and a Parsing Algorithm

A Watson–Crick (WK) context-free grammar, a context-free grammar with productions whose right-hand sides contain nonterminals and double-stranded terminal strings, generates complete double-stranded strings under Watson–Crick complementarity. In this paper, we investigate the simplification processes of Watson–Crick context-free grammars, which lead to defining Chomsky like normal form for Watson–Crick context-free grammars. The main result of the paper is a modified CYK (Cocke–Younger–Kasami) algorithm for Watson–Crick context-free grammars in WK-Chomsky normal form, allowing to parse double-stranded strings in O(n^6) time.

The effect of dephasing on superadiabatic single-qubit rotation gates

To implement quantum gates stimulated Raman adiabatic passage (STIRAP) can be used. This STIRAP requires high Rabi frequencies and to overcome this problem we use superadiabatic approach. Our model is a tripod consisting of four-level system driven by three resonant fields. These fields are modulated by Gaussian pulses with different amplitudes, phases and time delays. We investigate the robustness of our model against dephasing which are caused by collisions or phase fluctuations of the fields.

Superadiabatic STIRAP: Population Transfer and Quantum Rotation Gates

Stimulated Raman Adiabatic Passage is an important process for population transfer as well as for implementing quantum gates. This process requires large Rabi frequencies, which is an undesirable in many experimental applications. To overcome this problem transitionless (superadiabatic) STIRAP was proposed. In this paper we study the role of superadiabatic STIRAP in two examples, population transfer and quantum rotation gates. The effect of dephasing was also investigated by computing the fidelity. We have shown that the damping of the excited state has a little effect but the dephasing of the ground state leads to imperfect population transfer and imperfect rotation gates.

The computational power of Watson-Crick grammars: Revisited

A Watson-Crick finite automaton is one of DNA computational models using the Watson-Crick complementarity feature of deoxyribonucleic acid (DNA). We are interested in investigating a grammar counterpart of Watson-Crick automata. In this paper, we present results concerning the generative power of Watson-Crick (regular, linear, context-free) grammars. We show that the family of Watson-Crick context-free languages is included in the family of matrix languages.

Computational Properties of Watson-Crick Context-Free Grammars

Deoxyribonucleic acid, or popularly known as DNA, continues to inspire many theoretical computing models, such as sticker systems and Watson-Crick grammars. Sticker systems are the abstraction of ligation processes performed on DNA, while Watson-Crick grammars are models motivated from Watson-Crick finite automata and Chomsky grammars. Both of these theoretical models benefit from the Watson-Crick complementarity rule. In this paper, we establish the results on the relationship between Watson-Crick linear grammars, which is included in Watson-Crick context-free grammars, and sticker systems. We show that the family of arbitrary sticker languages, generated from arbitrary sticker systems, is included in the family of Watson-Crick linear languages, generated from Watson-Crick linear grammars.