Representations and Properties of Generalized ArA_r Statistics

A generalization of $A_r$ statistics is proposed and developed. The generalized $A_r$ quantum statistics is completely specified by a set of Jacobson generators satisfying a set of triple algebraic relations. Fock-Hilbert representations and Bargmann-Fock realizations are derived.Comment: 12 pages, to appear in IJMPA (2006

Three dimensional quantum key distribution in the presence of several eavesdroppers

Quantum key distribution based on encoding in three dimensional systems in the presence of several eavesdroppers is proposed. This extends the BB84 protocol in the presence of many eavesdroppers where two-level quantum systems (qubits) are replaced by three-level systems (qutrits). We discuss the scenarios involving two, three and four complementary bases. We derive the explicit form of Alice and Bob mutual information and the information gained by each eavesdropper. In particular, we show that, in the presence of only one eavesdropper, the protocol involving four bases is safer than the other ones. However, for two eavesdroppers, the security is strongly dependent on the attack probabilities. The effect of a large number of eavesdroppers is also investigated

Extended Weyl-Heisenberg algebra, phase operator, unitary depolarizers and generalized Bell states

Finite dimensional representations of extended Weyl-Heisenberg algebra are studied both from mathematical and applied viewpoints. They are used to define unitary phase operator and the corresponding eigenstates (phase states). It is also shown that the unitary depolarizers can be constructed in a general setting in terms of phase operators. Generation of generalized Bell states using the phase operator is presented and their expressions in terms of the elements of mutually unbiased bases are given

Quantum discord in photon added Glauber coherent states of GHZ{\rm GHZ}-type

We investigate the influence of photon excitations on quantum correlations in tripartite Glauber coherent states of Greenberger-Horne-Zeilinger type. The pairwise correlations are measured by means of the entropy-based quantum discord. We also analyze the monogamy property of quantum discord in this class of tripartite states in terms of the strength of Glauber coherent states and the photon excitation order.Comment: 20 page

Pairwise quantum and classical correlations in multi-qubits states via linear relative entropy

The pairwise correlations in a multi-qubit state are quantified through a linear variant of relative entropy. In particular, we derive the explicit expressions of total, quantum and classical bipartite correlations. Two different bi-partioning schemes are considered. We discuss the derivation of closest product, quantum-classical and quantum-classical product states. We also investigate the additivity relation between the various pairwise correlations existing in pure and mixed states. As illustration, some special cases are examined.Comment: 19 pages, To appear in International Journal of Quantum Informatio

Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system $[ 1]$. We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states \`{a} la Gazeau-Klauder and those \`{a} la Klauder-Perelomov, we derive the generalized intelligent states in analytical ways

Bipartite and Tripartite Entanglement of Truncated Harmonic Oscillator Coherent States via Beam Splitters

We introduce a special class of truncated Weyl-Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy

Reduced Dynamics from the Unitary Group to Some Flag Manifolds : Interacting Matrix Riccati Equations

In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equation satisfies. Our result is a natural generalization of the paper {\bf Chaturvedi et al} (arXiv : 0706.0964 [quant-ph]).Comment: Latex ; 13 pages ; no figur